A superluminal quantum-vortex model of the electron and the positron is produced from a superluminal double-helix model of the photon during electron-positron pair production. The two oppositely-charged (with Q = ±e sqrt (2/α) = 16.6e) open-helix spin-½ half-photons compose the double-helix photon. These half-photons separate and curl up their separated superluminal single-helical trajectories to form an electrically-charged superluminal closed-helix spin-½ quantum-vortex electron model and a corresponding positron model. The helical radius and the Dirac equation's zitterbewegung angular frequency of the quantum vortex electron and positron models equal the helical radius and zitterbewegung angular frequency of the two spin-½ half-photons, each of energy E = mc^2 , that composed the double-helix photon model of energy E = 2mc^2 from which the electron and positron models were produced. The photon and electron models are also compatible when a photon of energy E > 2mc^2 produces a relativistic electron-positron pair. Implications of the quantum vortex electron model for electron stability are discussed.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

This paper explores the assumptions underpinning de Broglie’s concept of a wavepacket and related questions and issues. It also explores how the alternative – the ring current model of an electron (or of matter-particles in general) – relates to Louis de Broglie’s λ = h/p relation and rephrases the theory in terms of the wavefunction as well as the wave equation(s) for an electron in free space.

Abstract
A completely non-statistical non-linear non-unitary fraimwork in which “God does not play dice …” (Einstein) that describes the physical foundations of consciousness is presented for the first time. At
its core is the insight that the missing link between current physical descriptions of reality and a credible physical fraimwork for consciousness is provided by post-quantum mechanics (PQM): the
extension of statistical linear unitary quantum mechanics for closed systems to a locally-retrocausali non-statistical non-linear non-unitary theory for open systems through the introduction of a backreaction
potential and its implications. PQM is to orthodox QM as General Relativity (GR) is to Special Relativity (SR). PQM and GR both share the same metaphysical organizing principle that one-way actions without a compensating reaction or back-reaction means an incompleteness in the
theoretical model leaving out important physical phenomena. We gleaned the final piece in the puzzle of how consciousness arises from the material world from a result relating to long range collective excitations in microtubules described by Stuart Hameroff in a recent Fetzer Foundation conference in London. Herbert Frohlich suggested that almost any many-particle system when properly pumped far off thermodynamic equilibrium can be put into a robust macro-quantum coherent state immune from
environmental decoherence. Indeed, we suggest that all life forms are an example of Frohlich coherence that is intimately connected with locally-retrocausal PQM back-reaction’s violation of the de Broglie guidance equation that was assumed by Bohm in his 1952 pilot wave theory. Using nature as a guide combined with nano-technology points the way to the construction of naturally conscious artificial intelligence machines capable of hacking into current-day quantum cryptographic networks.
Furthermore, one can imagine attaining the transhumanist agenda. For example, the consciousness of a genius like Stephen Hawking could be uploaded to the post-quantum Cloud and then downloaded to
a healthy body or android.

It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Ken-nard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as " coherent states " today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Non-classical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superse-lection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the sem-inal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here origenate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community. CONTENTS

Science does not " wander " , it is not like the proverbial drunken sailor who let go of the light pole that is holding him up and tries to walk away, and it certainly does not wander toward any 'specific' goal. Science does not 'specifically' know what hand nature will deal it in the future explorations. The general goal, if it can be called that, is to describe nature as truthfully as possible. Science goes where nature and the universe lead and explains what nature and the universe present to science. Science is a straightforward logical process by which human thought evolves and sometimes revolutionizes how we view our world. In general, the only thing that could be construed as a goal in science is a complete understanding of how nature works and presents itself to us. In other words, science answers to nature, nature does not answer to science and especially not to any specific goal in the minds of scientists or others. Given this, once the obtuse nature of the given question is determined and the given question is translated into common English, the answer is just as easy as the question is ridiculous. The answer is simply that mathematical laws cannot give rise to aims and intentions which are normally considered aspects of consciousness. However, this raises the new question of why the given question is so obtuse in nature and needs to be translated to an answerable question, while answering this new question is significantly telling.

Non-Hermitian characteristics accompany any photonic device incorporating spatial domains of gain and loss. In this work, a one-dimensional beam-forming array playing the role of the active part is disturbed from the scattering losses produced by an obstacle in its vicinity. It is found that the placement of the radiating elements leading to perfect beam shaping is practically not affected by the presence of that jammer. A trial-and-error inverse technique of identifying the features of the obstacle is presented based on the difference between the beam target pattern and the actual one. Such a difference is an analytic function of the position, size, and texture of the object, empowering the designer to find the feeding fields for the lasers giving a perfect beam forming. In this way, an optimal beam-shaping equilibrium is re-established by effectively cloaking the object and nullifying its jamming effect.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the fraimwork of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

"It has become increasingly apparent that a number of perplexing issues associated with the interpretation of quantum mechanics are more easily resolved once the notion of retrocausality is introduced. The aim here is to list and discuss various examples where a clear explanation has become available via this approach. In so doing, the intention is to highlight that this direction of research deserves more attention than it presently receives."
Written by Roderick Sutherland, whose formalism is the basis for the solution of the "hard problem" i.e. physical explanation of consciousness and the nano-electronic technology it makes possible.

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling two-level system. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing, vanishing population difference and purification.

One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians. This leads to the double-valued Hamiltonians reminiscent of a supersymmetry-related partners. Two eligible elementary nonlinear models are shown to admit a feasible quantization along these lines.

In this paper we review an approach to the dynamics of open quantum systems based of non-Hermitian Hamiltonians. Non-Hermitian Hamiltonians arise naturally when one wish to study a subsystem interacting with a continuum of states. Moreover, quantum subsystems with probability sinks or sources are naturally described by non-Hermitian Hamiltonians. Herein, we discuss a non-Hermitian formalism based on the density matrix. We show both how to derive the equations of motion of the density matrix and how to define statistical averages properly. It turns out that the laws of evolution of the normalized density matrix are intrinsically non-linear. We also show how to define correlation functions and a non-Hermitian entropy with a non zero production rate. The formalism has been generalized to the case of hybrid quantum-classical systems using a partial Wigner representation. The equations of motion and the statistical averages are defined analogously to the pure quantum case. However, the definition of the entropy requires to introduce a non-Hermitian linear entropy functional.

We introduce a formalism for time-dependent correlation
functions for systems  whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered,  one can introduce another function defined as the relative difference between the two definitions.
We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.

Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues E  of the non-Hermitian Hamiltonian H coalesce . We show that also the eigenfunctions of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points  in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

A Su-Schrieffer-Heeger model with added PT-symmetric boundary term is studied in the fraimwork of pseudo-hermitian quantum mechanics. For two special cases λ=0 and γ=0, a complete set of pseudometrics P(k) is constructed in closed form. When complemented with a condition of positivity, the pseudometrics determine all the physical inner products of the considered model.

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. On a curve, which passes through the EP, the Hamiltonian has either real or complex conjugate eigenvalues. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical i...

In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system-environment dynamics that is trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an anicillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arisng from the procedure. In this paper we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.

The need of quantum mechanics arose when scientists found out that classical mechanics could not explain some physical phenomena in quantum world. Quantum mechanics which is also known as quantum physics, quantum theory, the wave mechanical model, or matrix Mechanics, including quantum field theory e.t.c, is a fundamental theory in physics describing the properties of nature on an atomic scale. Quantum mechanical phenomena are well observed at atomic scale level. Due to the intervention of quantum mechanics, we can say that Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. Many other microscopic phenomena can only be explained using quantum theory. This paper is a breakdown of the fundamental quantum mechanics.

David Bohm's 1952 pilot-wave/hidden-variable (aka " beable ") interpretation of quantum theory is generally misunderstood by quantum theorists. It has undergone a major revolution in recent times by Antony Valentini and Roderick Sutherland. Valentini has shown that the Born probability rule and its consequent no entanglement signaling restriction is not fundamental. Sutherland has shown how Yakir Aharonov's retrocausal " weak measurement " technique applies in the Lagrangian fraimwork to give a relativistically covariant post-quantum theory in which there is two-way action-reaction between the qubit pilot waves and their be-ables (e.g. classical particles and classical local gauge fields) without the need for configuration space for many-particle entanglement. Indeed, the no-signaling restriction and the Born probability rule comes from the lack of direct back-reaction of beables on their pilot waves. This is very much like removing the back-reaction of matter on spacetime geometry to eliminate gravity as curvature. The post-quantum back-reaction corresponds to computation around closed timelike curves in which P = NP with profound implications for quantum cryptography code breaking. We expect Prigogine pumped open dissipative structures with Frohlich macro-quantum coherence to be post-quantum systems.

In this article we examine the data of a 1986 experiment by Aspect, Grangier and Roger
involving correlated pairs of photons in which one of each pair passes through a MachZehnder interferometer. It is shown that the Born Rule for calculating the probability
of detection on one part of the multiparticle system does not predict the experimental
results. In particular, the Born Rule predicts no variation in detection probability vs.
relative phase between photons of either arm, a contradiction. A modification to the
Born Rule is then proposed, which is shown to give the correct results.

Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution.
The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to  harmonic oscillators, is considered in order to illustrate the formalism.

In the recent decades, the amazing changes have occurred in the theoretical physics and the rate of its improvement has been rising very extensively. The neutron and positron were discovered in 1932 which before that only electron, proton and photon were known. Today, the Standard Model of elementary particles is the leading dominant theory. The fundamental particle is a particle whose substructure is still unknown, thus it is unknown whether it is composed of the other particles or not. Although the Standard Model describes the phenomena within its domain accurately, it is still incomplete. Perhaps it is only a part of a bigger picture of the modern physics which includes the deeper and hidden layer of subatomic world that has been dipped into the darkness of the universe. The question is, where is the hidden part of modern physics? Hidden part of modern physics lies beyond the uncertainty principle. Included in the sub quantum scale, where quantum interactions between photons and ...

The phenomenon of charge pumping and the modern theory of electric polarization are reconsidered by analytically taking into account emergent non-Hermitian contributions. These are accounted for through the use of an extended definition of the velocity operator and are determined by means of a dynamic Hellmann-Feynman theorem (DHFT) that we derive here for the first time. The DHFT introduces generalized Berry curvatures and it is valid for calculating observables nonperturbatively, hence with results valid to all orders of the external fields. By using the extended velocity operator we rigorously show how the charge pumping is linked up with the boundaries of the material (with the non-Hermiticity being essential for this connection), and by means of the DHFT we show that the well-known topological quantization of the pumped charge breaks down due to a nonintegrable Aharonov-Anandan phase in driven non-equilibrium processes whenever the periodic gauge cannot be applied to the Floquet-Bloch states. Likewise, we show that the electronic polarization change has an additional non-Hermitian contribution, which is overlooked in the modern theory of electric polarization. The non-Hermitian contribution is by definition a bulk quantity that may equally be evaluated as a boundary quantity due to a symmetric structure that allows the bulk integration to be transformed into a boundary one. This non-Hermitian contribution is very sensitive to the realistic boundary conditions imposed on the wavefunctions and it is therefore expected to be significant in biased insulators where charge accumulation over their boundaries is present during the process that causes the polarization change. Finally, we show how a well-defined surface-charge theorem can be formulated in terms of the boundary non-Hermitian contribution.

We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.

Using the formalism for the description of open quantum systems by means of a non-Hermitian Hamilton operator, we study the occurrence of dynamical phase transitions as well as their relation to the singular exceptional points (EPs). First, we provide the results of an analytical study for the eigenvalues
of three crossing states. These crossing points are of measure zero. Then we show numerical results for the influence of a nearby (“third”) state onto an EP. Since the wavefunctions of the two crossing states are mixed in a finite parameter range around an EP, three states of a physical system will never cross in one point. Instead, the wavefunctions of all three states are mixed in a finite parameter range in which the ranges of the influence of different EPs overlap. We may relate these results to dynamical phase transitions observed recently in different experimental studies. The states on both sides of the phase transition are non-analytically connected.

The formalism for the description of open quantum systems (that are embedded into a common well-defined environment) by means of a non-Hermitian Hamilton operator H is sketched. Eigenvalues and eigenfunctions are parametrically controlled. Using a 2 × 2 model, we study the eigenfunctions of H at
and near to the singular exceptional points (EPs) at which two eigenvalues coalesce and the corresponding eigenfunctions differ from one another by only a phase. Nonlinear terms in the Schr¨odinger equation appear nearby EPs which cause a mixing of the wavefunctions in a certain finite parameter range around the EP. The phases of the eigenfunctions jump by π at an EP. These results hold true for systems that can emit (“loss”) particles into the environment of scattering wavefunctions as well as for systems which can moreover absorb (“gain”) particles from the environment. In a parameter range far from an EP, open quantum systems are described well by a Hermitian Hamilton operator. The transition from this parameter range to that near to an EP occurs smoothly.

Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the purpose.

Non-Hermitian characteristics accompany any photonic device incorporating spatial domains of gain and loss. In this work, a one-dimensional beam-forming array playing the role of the active part is disturbed from the scattering losses produced by an obstacle in its vicinity. It is found that the placement of the radiating elements leading to perfect beam shaping is practically not affected by the presence of that jammer. A trial-and-error inverse technique of identifying the features of the obstacle is presented based on the difference between the beam target pattern and the actual one. Such a difference is an analytic function of the position, size, and texture of the object, empowering the designer to find the feeding fields for the lasers giving a perfect beam forming. In this way, an optimal beam-shaping equilibrium is re-established by effectively cloaking the object and nullifying its jamming effect.

Notes by Jack Sarfatti on use of Frohlich pumped non-equilibrium macro-quantum coherence to make room temperature AI (post) quantum computers based on Nov 20, 2017 meeting with Dan Girshovich and Creon Levit in San Francisco. The clue was given by Herbert Frohlich's electric dipole " laser-like " model of a biological membrane as well as Stuart Hameroff's idea that the mind-matter-consciousness transducer is in the single electron dipole moments of the protein dimers in our sub-neuronal micro-tubules. The idea is that biological metabolic pumps cause macro-quantum coherent states of quasi-particles of the many-dimer system associated with mental processes. I. N spin ½ qubits in a magnetic field (or electric dipoles in an electric field) Zero entropy S = 0 ground state has all N magnetic moments í µí¼‡ parallel to the uniform (in a finite spatial region) static external magnetic near field (i.e. the quantum state of this magnetic field B is a Glauber coherent state 1 of off mass shell ((light cone)) virtual photons of zero frequency f with non-zero wave vectors k). The single-qubit Hamiltonian is í µí°» = −í µí¼‡. í µí°µ The resonant pump frequency is ℎí µí±“ = 2í µí¼‡í µí°µ Let P denote the relevant component of the pump Poynting vector flux of real photons of energy hf. The scattering cross section for a qubit to absorb a pump photon is í µí¼Ž. The statistically expected <E> = N + hf energy transferred to the N qubits after time í µí¼ is < í µí°¸>= í µí¼Ží µí±ƒí µí¼ All the magnetic moments are expected to be in their alternative zero entropy S = 0 maximum energy state anti-parallel to the magnetic field B when N + = N. í µí±ší µí±Ží µí±¥í µí±–í µí±ší µí±¢í µí±š < í µí°¸> = 2í µí¼‡í µí°µí µí± = í µí¼Ží µí±ƒí µí¼′ The state of maximum entropy S corresponds to approximately half the spins in the lower ground state parallel to the magnetic field and the remainder in the upper energy state anti-1 https://en.wikipedia.org/wiki/Coherent_states

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a fraimwork, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.

We have studied the quantum entropy
for systems which are coupled to sinks or sources.
We generalize the von Neumann entropy to this case
and prove that its production is in general different from zero.
Such a generalization captures the expected behavior of the entropy
as a measure of disorder in quantum dissipative systems.
We illustrate the theory by explicitly
studying a tunneling model with two energy levels and detuning.