System Of Quantum Particles Research Articles

Inequality in the Distribution of Wealth and Income as a Natural Consequence of the Equal Opportunity of All Members in the Economic System Represented by a Scale-Free Network

The purpose of this work is to examine the nature of the historically observed and empirically described by the Pareto law inequality in the distribution of wealth and income in an economic system. This inequality is presumed to be the result of unequal opportunity by its members. An analytical model of the economic system consisting of a large number of actors, all having equal access to its total wealth (or income) has been developed that is formally represented by a scale-free network comprised of nodes (actors) and links (states of wealth or income). The dynamic evolution of the complex network can be mapped in turn, as is known, into a system of quantum particles (links) distributed among various energy levels (nodes) in thermodynamic equilibrium. The distribution of quantum particles (photons) at different energy levels in the physical system is then derived based on statistical thermodynamics with the attainment of maximal entropy for the system to be in a dynamic equilibrium. The resulting Planck-type distribution of the physical system mapped into a scale-free network leads naturally into the Pareto law distribution of the economic system. The conclusions of the scale-free complex network model leading to the analytical derivation of the empirical Pareto law are multifold. First, any complex economic system behaves akin to a scale-free complex network. Second, equal access or opportunity leads to unequal outcomes. Third, the optimal value for the Pareto index is obtained that ensures the optimal, albeit unequal, outcome of wealth and income distribution. Fourth, the optimal value for the Gini coefficient can then be calculated and be compared to the empirical values of that coefficient for wealth and income to ascertain how close an economic system is to its optimal distribution of income and wealth among its members. Fifth, in an economic system with equal opportunity for all its members there should be no difference between the resulting income and wealth distributions. Examination of the wealth and income distributions described by the Gini coefficient of national economies suggests that income and particularly wealth are far off from their optimal value. We conclude that the equality of opportunity should be the fundamental guiding principle of any economic system for the optimal distribution of wealth and income. The practical application of this conclusion is that societies ought to shift focus from policies such as taxation and payment transfers purporting to produce equal outcomes for all, a goal which is unattainable and wasteful, to policies advancing among others education, health care, and affordable housing for all as well as the re-evaluation of rules and institutions such that all members in the economic system have equal opportunity for the optimal utilization of resources and the distribution of wealth and income. Future research efforts should develop the scale-free complex network model of the economy as a complement to the current standard models.

How to Partition a Quantum Observable.

We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy that is consistent with the laws of thermodynamics.

Planar two-region multi-partite maximally entangled states

In entanglement theory, there are different methods to consider one state being more entangled than another. The “maximally” entangled states in a multipartite system can be defined from an axiomatic perspective. According to different criteria for selection, there are many specific types of quantum maximally entangled states, such as absolutely maximally entangled state, planar maximally entangled state and so on. In this paper we propose a new type of maximally entangled states, the planar two-region multipartite maximally entangled state. The requirement condition of this maximally entangled state is weak than that of the absolutely maximally entangled state and different from that of the planar maximally entangled state. We show that there are the two-region four-partite maximally entangled states in 4-qubit and 7-qubit planar systems, although there is no absolutely maximally entangled state in these systems. It is proved that there are the planar two-region four-partite maximally entangled states in both even particle quantum systems and odd particle quantum systems. Additionally, based on some planar two-region four-partite maximally entangled states, the new planar two-region four-partite maximally entangled states are generated. We also provide some important examples of the planar two-region multi-partite maximally entangled states.

Research on the Compatibility of Quantum Science and Marxist Philosophy

As an epoch-making achievement in the field of natural science, the scientific principles of quantum mechanics, such as nonlocality, entanglement and decoherence, and role at a distance, have triggered many different interpretations and controversies in the field of philosophy, among which idealism, metaphysics, and agnosticism are based on which to question or even deny dialectical materialism. Marxist philosophy has always closely interacted with natural science. In the face of new and old propositions in quantum mechanics, such as uncertainty principle, quantum tunneling, large distance zero interaction measurement, and Poincare regression of multi particle quantum system, we can promote its compatibility with the new world outlook and methodology of quantum science in the intertextuality interpretation. Quantum mechanics reveals the "intermediate phenomenon" in the process of understanding the micro world, highlighting the dialectical characteristics of materialistic epistemology; It emphasizes probability, but denies that uncertainty is subjective conjecture, defending the objectivity of existence; For the movement and change of things, the status of the contingency category has been improved and the linear causality has been exceeded, but the existence of universal and inevitable connection has not been fundamentally denied.

Upper bound efficiencies for work generation from the energy of confined systems of quantum particles

The maximum amount of work extraction from confined particles energy is treated for a larger class of particles than the usual case of boltzons and photons. The treatment does not restrict to exergy evaluation since real-world processes take place in finite time. Both reversible and endoreversible work extraction is considered. The maximum extractable work is estimated in case that the equilibrium of the particle system with the environment is not reached during work extraction. This result is different for bosons or fermions having non-zero rest mass in the non-relativistic limit and for zero rest mass or non-zero rest mass particles in the extreme relativistic limit, respectively. For particles obeying spontaneous creation and annihilation the exergy content cannot be properly defined. The exergy concept makes sense for confined particles for which very slow (flowing) filling and emptying processes may be imagined. The Carnot efficiency is not a proper upper bound for the conversion of confined thermal radiation into work but it may be used as a safe superior (but less accurate) limit in this case.

Three-dimensional wormhole with cosmic string effects on eigenvalue solution of non-relativistic quantum particles

In this paper, we explore the quantum system of non-relativistic particles in a unique scenario: a circularly symmetric and static three-dimensional wormhole space-time accompanied by cosmic strings. We focus on a specific case where the redshift function varPhi (r) to be zero and defining the shape function as A(r)=frac{b}{r^2}. After establishing this background space-time, we investigate the behavior of a harmonic oscillator within the same wormhole context. By doing so, we observe the effects of the cosmic string and wormhole throat radius on the eigenvalue solution of the oscillator’s eigenvalue problem. The primary finding is that these cosmic features lead to modifications in the energy spectrum and wave functions of the system, breaking the degeneracy of energy levels that would typically be present in a more conventional setting. As a particular case, we present the specific energy level E_{1,ell } and the corresponding wave function psi _{1,ell }, which are associated with the ground state of the quantum system. These results highlight the fascinating and unique properties of the harmonic oscillator in the background of a circularly symmetric, static wormhole space-time with cosmic strings.

Many body density of states of a system of non interacting spinless fermions

The modeling of out-of-equilibrium many-body quantum systems requires to go beyond low-energy physics and single or few bodies densities of states. Many-body localization, presence or lack of thermalization and quantum chaos are examples of phenomena in which states at different energy scales, including highly excited ones, contribute to dynamics and therefore affect the system’s properties. Quantifying these contributions requires the many-body density of states (MBDoS), a function whose calculation becomes challenging even for non-interacting identical particles due to the difficulty to enumerate accessible states while enforcing the exchange symmetry. In the present work, we introduce a new approach to evaluate the MBDoS in the general case of non-interacting systems of identical quantum particles. The starting point of our method is the principal component analysis of a filling matrix F describing how N particles can be distributed into L single-particle energy levels. We show that the many body spectrum can be expanded as a weighted sum of singular vectors of the filling matrix. The weighting coefficients only involve renormalized energies obtained from the single body spectrum. We illustrate our method in two classes of problems that are mapped into spinless fermions : (i) non-interacting electrons in a homogeneous tight-binding model in 1D and 2D, and (ii) interacting spins in a chain under a transverse field.

Energetics of a self-gravitating quantum system of charged particles

Extending our model of Newtonian Quantum Gravity (NQG) in a self-gravitating system (Lotte B. K. and Mishra S., Mod. Phys. Lett. A, 35 (2020) 2050081), we study here the energetics of a charged self-gravitating quantum many-particle system. The model is based on the use of the uncertainty principle and the incorporation of necessary relativistic corrections. From the resulting ground state energy we have derived the effective radius of the system of charged particles, after it gets collapsed under its own gravity. Additional results like the Hawking temperature and the Buchdahl-Andréasson (BA) limit for this system are also explored. We further show a possible link of this collapsed system of self-gravitating charge particles, with the notion of a charged black hole.

Localization by particle–hole symmetry breaking: a loop expansion

Localization by a broken particle–hole (PH) symmetry in a random system of non-interacting quantum particles is studied on a d-dimensional lattice. Our approach is based on a chiral symmetry argument and the corresponding invariant measure, where the latter is described by a Grassmann functional integral. Within a loop expansion we find for small loops diffusion in the case of PH symmetry. Breaking the PH symmetry results in the creation of random dimers, which suppress diffusion and lead to localization on the scale , where D is the effective diffusion coefficient at PH symmetry and μ is the parameter related to PH symmetry breaking.

Two-sided Bogoliubov inequality to estimate finite size effects in quantum molecular simulations

We generalise the two-sided Bogoliubov inequality for classical particles (Delle Site et al. in J Stat Mech Theory Exp 083201, 2017 to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower bounds for the free energy difference associated with the partitioning of a large system into smaller, independent subsystems. From a thermodynamic modelling point of view, the free energy difference determines the finite size correction needed to consistently treat a small system as a representation of a large system. Applications of the bounds to quantify finite size effects are ubiquitous in physics, chemistry, material science, or biology, to name just a few; in particular, it is relevant for molecular dynamics simulations in which a small portion of a system is usually taken as representative of the idealized large system.

Do atoms age?

Time evolution generically entangles a quantum state with environmental degrees of freedom. The resulting increase in entropy changes the properties of that quantum system leading to “aging”. It is interesting to ask if this familiar property also applies to simple, single particle quantum systems such as the decay of a radioactive particle. We propose a test of such aging in an ion clock setup where we probe for temporal changes to the energies of the electronic state of an ion containing a radioactive nucleus. Such effects are absent in standard quantum mechanics and this test is thus a potent null test for violations of quantum mechanics. As a proof of principle, we show that these effects exist in causal non-linear modifications of quantum mechanics.

Transition rates of noninteracting quantum particles from the Widom insertion formula

Transition rates among different states in a system of noninteracting quantum particles in contact with a heat reservoir include the factor 1∓n[over ¯]_{i}, with a minus sign for fermions and a plus sign for bosons, where n[over ¯]_{i} is the average occupation number of the final state. It is shown that this factor can be related to the difference of the chemical potential from that of an ideal classical mixture; this difference is formally equivalent to the excess chemical potential in a classical system of interacting particles. Using this analogy, Widom's insertion formula is used in the calculation of transition rates. The result allows an alternative derivation of quantum statistics from the condition that transition rates depend only on the number of particles in the target energy level. Instead, if transition rates depend on the particle number only in the origin level, the statistics of ewkons is obtained; this is an exotic statistics that can be applied to the description of dark energy.

Conformal quantum mechanics & the integrable spinning Fishnet

In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ, dot{ell} of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆k, ℓk, dot{ell} k) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed mathcal{N} = 4 and mathcal{N} = 2 supersymmetric theories.

The law of large numbers for quantum stochastic filtering and control of many-particle systems

There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Scrodinger equations or Hartree equations, or Gross-Pitaevski equations. In this paper we extend some of these convergence results to a stochastic framework. Concretely we work with the Belavkin stochastic filtering of many particle quantum systems. The resulting limiting equation is an equation of a new type, which can be seen as a complex-valued infinite dimensional nonlinear diffusion of McKean-Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.

The law of large numbers for quantum stochastic filtering and control of many-particle systems

Существует обширная литература, где рассматривается динамический закон больших чисел для систем квантовых частиц, т. е. выводится уравнение, описывающее предельное поведение отдельных частиц внутри большого ансамбля одинаковых взаимодействующих частиц. Полученные уравнения обычно называют нелинейными уравнениями Шредингера, или уравнениями Хартри, или уравнениями Гросса-Питаевского. Дано стохастическое обобщение некоторых из этих результатов, касающихся сходимости. Рассмотрена стохастическая фильтрация Белавкина для многочастичных квантовых систем. Полученное предельное уравнение - это уравнение нового типа, которое можно трактовать как комплекснозначную бесконечномерную нелинейную диффузию типа Маккина-Власова. Этот результат является ключевым для теории квантовых игр среднего поля, разработанной автором в предыдущей работе.

Efficient sampling of thermal averages of interacting quantum particle systems with random batches.

An efficient sampling method, the pmmLang + RBM, is proposed to compute the quantum thermal average in the interacting quantum particle system. Benefiting from the random batch method (RBM), the pmmLang + RBM has the potential to reduce the complexity due to interaction forces per time step from O(NP2) to O(NP), where N is the number of beads and P is the number of particles. Although the RBM introduces a random perturbation of the interaction forces at each time step, the long time effects of the random perturbations along the sampling process only result in a small bias in the empirical measure of the pmmLang + RBM from the target distribution, which also implies a small error in the thermal average calculation. We numerically study the convergence of the pmmLang + RBM and quantitatively investigate the dependence of the error in computing the thermal average on the parameters such as batch size, time step, and so on. We also propose an extension of the pmmLang + RBM, which is based on the splitting Monte Carlo method and is applicable when the interacting potential contains a singular part.

Quantum system: Wave function, entanglement and the uncertainty principle

A definition of entanglement based on the overlap of wave functions of identical particles is proposed. A definition of a quantum system of particles related to their entanglement with each other and the environment is proposed. It is shown that in the general case, the uncertainty principle cannot be formulated for a system of quantum particles in the form of a single inequality.

The Random Batch Method for $N$-Body Quantum Dynamics

This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by the interaction with $p 1$ and independent of the Planck constant $\hbar$.

Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low-energy regime

I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, statistical transmutation operators that are genuinely unitary are obtained, putting bosons and fermions in a one-to-one correspondence without the need for a short-distance hard core. In the non-relativistic case, low-energy interactions for bosons yield, order by order, fermionic dual interactions that correspond to the standard low-energy expansion for fermions. In this way, interacting fermions and bosons are fully equivalent to each other at low energies. While the Bose-Fermi mappings do not depend on microscopic details, the resulting statistical interactions heavily depend on the kinetic energy structure of the respective Hamiltonians. These statistical interactions are obtained explicitly for a variety of models, and regularized and renormalized in the momentum representation, which allows for theoretically and computationally feasible implementations of the dual theories. The mapping is rewritten as a gauge interaction, and one-dimensional anyons are also considered.

The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas

This paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in Rd. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a boundary condition at the border of a ‘box’). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of diameter a>0. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. As a justification of this concept, we prove that for d=2, any FK-DLR functional is shift-invariant, regardless of whether it is unique or not. This yields a quantum analog of results previously achieved by Richthammer.