Quantum Field Systems Research Articles

Realization of quantum secure direct communication by Kitaev Abelian anyons

The quantum secure direct communication (QSDC) is provably secure and has a high capacity. The QSDC protocols are usually experimented in photon systems. Here we propose four schemes to realize the QSDC in the Kitaev Abelian anyon model: 1) the two-step scheme, 2) 2⊗2 dimensional superdense coding scheme, 3) the hyperentanglement-assisted one-step scheme and 4) one-time pad scheme. Our work provides a possibility to implement the quantum secure direct communication in many-body systems and gives a new research perspective of the quantum information on the unitary evolution of quantum field systems.

Effective Lagrangian for the macroscopic motion of fermionic matter

We consider macroscopic motion of quantum field systems. The Zubarev statistical operator allows us to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of a functional integral. The effective Lagrangian is calculated explicitly for the fermionic systems interacting with dynamical gauge fields. Possible applications to physics of quark-gluon plasma are discussed. Published by the American Physical Society 2024

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

In both quantum and classical field systems, conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties. A broadly accepted approach to deriving conservation laws is built using Noether’s method. However, this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines. In the present study, we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems. In contrast to quantum systems, where particles are viewed as quantum fields, classical relativistic particle-field systems present specific challenges. These challenges arise from two sides. The first comes from the mass-shell constraint. To deal with the mass-shell constraint, the Euler–Lagrange–Barut (ELB) equation is used to determine the particle’s world lines in the four-dimensional (4D) Minkowski space. Besides, the infinitesimal criterion, which is a differential equation in formal field theory, is reconstructed by an integro-differential form. The other difficulty is that fields and particles depend on heterogeneous manifolds. To overcome this challenge, we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems. By applying a weak ELB equation to classical relativistic particle-field systems, we can systematically derive local conservation laws by examining the underlying symmetries of the system. Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

On Functional Hamilton–Jacobi and Schrödinger Equations and Functional Renormalization Group

We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the central equation of the functional renormalization group (FRG). These equations are formulated in D-dimensional coordinate and abstract (formal) spaces. Instead of extra coordinates or an FRG scale, a “holographic” scalar field Λ is introduced. The extra coordinate (or scale) is obtained as the amplitude of delta-field or constant-field configurations of Λ. For all the functional equations above a rigorous derivation of corresponding integro-differential equation hierarchies for Green functions (GFs) as well as the integration formula for functionals are given. An advantage of the HJ hierarchy compared to Schrödinger or WP hierarchies is that the HJ hierarchy splits into independent equations. Using the integration formula, the functional (arbitrary configuration of Λ) solution for the translation-invariant two-particle GF is obtained. For the delta-field and the constant-field configurations of Λ, this solution is studied in detail. A separable solution for a two-particle GF is briefly discussed. Then, rigorous derivation of the quantum HJ and the continuity functional equations from the functional Schrödinger equation as well as the semiclassical approximation are given. An iterative procedure for solving the functional Schrödinger equation is suggested. Translation-invariant solutions for various GFs (both hierarchies) on delta-field configuration of Λ are obtained. In context of the continuity equation and open quantum field systems, an optical potential is briefly discussed. The mode coarse-graining growth functional for the WP action (WP functional) is analyzed. Based on this analysis, an approximation scheme is proposed for the generalized WP equation. With an optimized (Litim) regulator translation-invariant solutions for two-particle and four-particle amputated GFs from approximated WP hierarchy are found analytically. For Λ=0 these solutions are monotonic in each of the momentum variables.

Interaction of Massless Dirac Field with 2D-Material in a Model Constructed in the Framework of Symanzik Approach

Based on the method proposed by Simanzik for modeling quantum field systems in inhomogeneous space-time, a model for the interaction of the Dirac massless field with a homogeneous isotropic plane is constructed. In this model, the process of scattering of particles on a plane is studied and the Casimir force for two parallel planes is calculated.

Switchback effect of holographic complexity in multiple-horizon black holes

In this paper, we use the “complexity equals action” (CA) conjecture to explore the switchback effect in the strongly-coupled quantum field theories with finite N and finite coupling effects. In the perspective of holography, this is equivalent to evaluating the CA complexity in a Vaidya geometry equipped with a light shockwave for a higher curvature gravitational theory. Based on the Noether charge formalism of Iyer and Wald, we obtain the slope of the complexity of formation in the small- and large-time approximations. By circuit analogy, we show that our results concur with the switchback effect of the quantum system. These results show that the switchback effect is a general feature of the CA complexity in stationary black holes and its existence is independent of the explicit gravitational theory as well as spacetime background. From the viewpoint of AdS/CFT, this also implies that the switchback effect is a general feature of the thermofield double state in the strongly-coupled quantum field systems with finite N and finite coupling effects. Moreover, we also illustrate that unlike the late-time complexity growth rate, the counterterm plays an important role in the study of the switchback effect.

The use of an adaptive mesh based on a quadtree for modeling the final state of a quantum field system under pulsed external action

The success of using mathematical models that determine the behavior of quantum field systems in parametric spaces critically depends on the level of optimization of the procedure of finding the solution. The paper considers the problem of calculating the density of carriers arising in graphene as a result of the action of a pulsed electric field. The basis of the model is a system of kinetic equations that provide the calculation of the residual distribution function. Its integration over momentum space gives the desired carrier density. The problem lies in the high computational complexity of covering the momentum space with a uniform mesh, which provides an accurate calculation of the density for various parameters of the field momentum. Moreover, the model does not contain criteria for determining satisfactory mesh parameters. The article proposes and implements a procedure for constructing an adaptive mesh in the form of a quadtree having a variable size of covering squares. The procedure is iterative and combined with the process of calculating the values of the distribution function.

Boltzmann entropy for quantum field systems

A way to construct Boltzmann entropy, i.e., the entropy as a function of a microscopic pure state, for quantum field systems is proposed. Operators that shift the field in wavevector space are used in the construction. By employing an assumption, it is shown that, for almost all states in the ensemble of pure states corresponding to a thermodynamic state, the value of the proposed Boltzmann entropy coincides with that of the thermodynamic entropy for the thermodynamic state. For general self-interacting fields, the Boltzmann entropy evolves with time under Hamiltonian dynamics, so that it is capable of characterizing the thermalization of isolated quantum field systems.

Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism

We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett--Garg inequality in Wigner form, which was recently presented in the literature, for three and $n$ distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Basing on the the Leggett--Garg inequality in Wigner form for $n$ distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to ``freezing'' of the system in the initial state. It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.

Unification of Thermo Field Kinetic and Hydrodynamics Approaches in the Theory of Dense Quantum–Field Systems

A formulation of nonequilibrium thermo-field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of the kinetics and hydrodynamics of the dense quantum field system with strongly-bound states are derived.

Numerical Modeling of Interaction and Decay Processes of Topological Vortices in Reversed Time

The paper studies T-symmetry properties of the well-known nonlinear sigma model (NSM), a class of quantum field systems in which physical fields are regarded as the coordinates of a certain manifold. Considers a symmetry property of the (2+1)-dimensional anisotropic O(3) NSM (n-field) with respect to time reversal. From the geometric point of view, O(3) NSM describes the dynamics of a single three-component isovectornthat takes on values in the Bloch sphere. The isovectorncan be identified with a point on the surface of a two-dimensional sphere and, therefore, corresponds to the element of a rotation group O(3). The anisotropy is selected in thez-axis direction and thus, the zero-energy states (vacuum states) of the model under investigation are equivalent to the point (the end of the isovectorn) at the poles of the Bloch sphere.О(3) NSМ has an exact solution in the form of topological solitons (vortices, quasi-particles) possessing a topological charge (the Hopf index). It was shown in [8] that, for certain rate values of their motion, the interacting topological solitons decay into localized perturbations. In this case, the property of preserving the total sum of the topological charge is revealed.In the present work, numerical modeling of interaction and decay processes of topological solitons of O(3) NSM in reversed time are carried out. It is shown that when there is time reversal, a complete restoration process of the initial state of the field of topological solitons by combining individual localized perturbations is observed. Thus, the paper confirms the property of T-invariance of O(3) NSM. To construct numerical models, are used methods of the theory of finite difference schemes, based on a specially developed algorithm for applying the properties of the stereographic projection of the Bloch sphere onto the complex plane. The developed method allows accurate calculations of the energy density of interacting vortex fields at each point of the stratified space. The paper proposes a software complex that allows us to conduct numerical studies of interaction processes of localized solutions of non-linear field-theoretical models in class O(3) NSM in reversed time.

Quantum field theory of photon–Dirac fermion interacting system in graphene monolayer

The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields.

Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class’ definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

Einstein–Podolsky–Rosen quantum simulations in nonclassical phase-space

We give a brief history of probabilistic quantum simulations of Einstein–Podolsky–Rosen paradoxes. This treats the early origins of the modern proposals using continuous variables, simulation methods using the positive-P representation, and current developments. Recent simulations treated include the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.

Scaling Without Conformal Invariants in the NonLocal Relativistic Quantum Systems in Living Cells

Since the 1948 the mathematical description of the so-called Casimir world as a part of the physical observed space-time in the relativistic sense is to be considered by the help of the Hamiltonian quantum field's theory and furthermore even it is based on the fine play between the continuity and the discrete too. The axiomatic-physical methods of the local quantum fields theory has given us the other possibility than the Lagrange quantum field's theory and precisely on this rigorously mathematical way to understand the singularities and the black holes, also the dark energy and the dark matter from one uniformly point of view. Aside from this, the essential difference is that external forces other than gravity, e.g. such as Casimir force, play a major role in the phenomena, i.e. there is not observed in our seeing world a local classical relativistic electromagnetic field potential Aμ(x). And also it is possible to describe the fundamental interactions between anyone concrete fundamental relativistic quantum field system with someone other or with the external and innerness material objects as a additional boundary conditions by the proving the fulfilling of the causality conditions and consider they as an external classical fields, and everyone internal background fields. At the first in his famous work To the Electrodynamics of moved bodies, Leipzig, 1905, Einstein has proved the possibility to understand the nature from the relativistic point of view in the classical physics. By the living cells as an object of the fundamental cryobiological researches i.e. in this case the metabolisms is minimal so that by the help of the axiomatic-physical methods by the relativistic theory of quantum fields systems considering as a Micro fields it is possible to be taken in the account the problem of a time's arrow at the microscopic level by the contemporary considerations of the quantum vacuum in the Casimir world as a ground state of anyone relativistic quantum system becomes a fixture by the lyophilized elementary living cells. So the possibility to understand the Hilbert space with indefinite metric for the further considerations the word elementary understands a one structure idealization of the living cells. Also the many

The theory of motion of quantum electromechanical plasmoid nanobots in a condensed-state medium

The theory of motion of quantum electromechanical plasmoid nanobots in a condensed-state medium is presented. The mechanism of a nanobot functioning is shown to be related to the quantum exchange between a nanoparticle and the quantum-field condensed-state system realized by a tangled (e − e +)-plasmoid pair. The operation of an (e − e +)-plasmoid is interpreted as a quantum analog of a fuel cell based on the nanoelectromechanical systems (NEMS) of a nanobot. It is the electrical and magnetic fields of force of the (e − e +)-plasmoid which control the quantum motion of the NEMS-based nanobot. This ensures its response to an external action and allows the respective physical tools to be designed in order to control self-motion of the NEMS-based nanobot in a material medium. Two available mechanisms of the relaxational self-motion of a nanobot in the condensed matter are shown: conversion of the internal quantum-mechanical energy of the nanobot into the electrical energy of a quantum (e − e +)-plasmoid and conversion of the electrical energy of a quantum (e − e +)-plasmoid into the mechanical energy of the nanobot’s motion in a material. These mechanisms prescribe a discrete manipulation of the NEMS-based nanobot in a material medium. The time, displacement, forces and power involved in the NEMS-based nanobot transportation are estimated.

Initial state and thermalization

Abstract We report recent results on the role of instabilities in the isotropization and thermalization of a longitudinally expanding system of quantum fields.

Mutual Information and Bose-Einstein Condensation

In this work we study an ideal bosonic quantum field system at finite temperature, and in a canonical and a grand canonical ensemble. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the von Neumann entropy that corresponds to the spatially separated subsystem (i.e. the geometric entropy) and then we subtract its extensive part which coincides with the thermal entropy of the subsystem. In the framework of the grand canonical description, we examine the influence of the underlying Bose-Einstein condensation on the behaviour of the mutual information, and we find that its derivative with respect to the temperature possesses a finite discontinuity at exactly the critical temperature.

From superoperator formalism to nonequilibrium Thermo Field Dynamics

Emphasizing that the specification of the representation space or the quasiparticle picture is essential in nonequilibrium quantum field system, we have constructed the unique unperturbed representation of the interaction picture in the superoperator formalism. To achieve it, we put the three basic requirements (the existence of the quasiparticle picture at each instant of time, the macroscopic causality and the relaxation to equilibrium). From the resultant representation follows the formulation of nonequilibrium Thermo Field Dynamics (TFD). The two parameters, the number distribution and excitation energy, characterizing the representation, are to be determined by the renormalization condition. While we point out that the diagonalization condition by Chu and Umezawa is inconsistent with the equilibrium theory, we propose a new renormalization condition as a generalization of the on-shell renormalization on the self-energy which derives the quantum transport equation and determines the renormalized excitation energy.

Can Entanglement Be Destroyed by Any Local Operation in Relativistic Quantum Field Theory?

This article investigates the nature of entangled correlations in algebraic quantum field theory (AQFT). We define a notion of local disentanglement, expressing the possibility of destroying entanglement by means of local operations. Contrary to the case of ordinary quantum mechanics, local disentanglement cannot be achieved in general in relativistic quantum field theory. However, we show that if the split property holds, there exists a local operation that can destroy entanglement between spacelike-separated quantum field systems.