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Nonequilibrium Phenomena in Strongly Correlated Systems
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Nonequilibrium Phenomena in Strongly Correlated Systems

A special issue of Particles (ISSN 2571-712X).

Deadline for manuscript submissions: closed (28 February 2019) | Viewed by 49406

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. David Blaschke

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Guest Editor
1. Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Poland
2. Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
3. Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-1328 Dresden, Germany
Interests: quantum field theory; quantum statistics; quark gluon plasma; heavy ion collisions; compact stars
Special Issues, Collections and Topics in MDPI journals
Dr. Alexandra Friesen

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Guest Editor
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
Special Issues, Collections and Topics in MDPI journals
Prof. Vladimir Morozov

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Guest Editor
Moscow Technological University, Moscow, Russia
Prof. Nikolay Plakida

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Guest Editor
Joint Institute for Nuclear Research Bogoliubov Laboratory of Theoretical Physics, 141980 Dubna, Joliot-Curie 6, Moscow reg., Russia
Prof. Gerd Röpke

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Guest Editor
1. Institut für Physik, Universität Rostock, D-18051 Rostock, Germany 2. National Research Nuclear University (MEPhI), 115409 Moscow, Russia

Special Issue Information

Nonequilibrium physics is of fundamental relevance for many phenomena, occurring at the highest energy densities, such as heavy ion collisions, and also for condensed matter physics and ultracold gases. Simple approaches, such as the Boltzmann equation, become questionable when strong correlations are formed in a system. The problems to be solved in different areas are connected with concepts to formulate a nonequilibrium theory. Time evolution, as described by kinetic equations, transport codes, or reaction networks, should also include the formation of correlations, and in particular bound states.

The aim of this Special Issue is to highlight the Zubarev method of the nonequilibrium statistical operator as a unifying concept to approach nonequilibrium phenomena in different fields of physics.

We are inviting contributions of general character, as well as from the different fields of applications, ranging from high-energy physics, where highly excited matter, possibly a quark–gluon plasma, is formed in heavy ion collisions to condensed matter physics. The contributions shall cover different topics of the many-body theory of strongly correlated systems, in particular, nonequilibrium phenomena in solids, liquids, and plasmas.

This Special Issue is dedicated to the memory of D. N. Zubarev (1917–1992), whose contributions to physics concerned, in particular, the method of green functions to treat strongly correlated systems and the method of the nonequilibrium statistical operator to describe nonequilibrium phenomena.

Prof. David Blaschke
Prof. Vladimir Morozov
Prof. Nikolay Plakida
Prof. Gerd Röpke
Dr. Alexandra V. Friesen
Guest Editors

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Published Papers (16 papers)

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Research

14 pages, 330 KiB  
Article
Nonequilibrium Pion Distribution within the Zubarev Approach
by David Blaschke, Gerd Röpke, Dmitry N. Voskresensky and Vladimir G. Morozov
Particles 2020, 3(2), 380-393; https://doi.org/10.3390/particles3020029 - 3 May 2020
Cited by 6 | Viewed by 2204
Abstract
We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence [...] Read more.
We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
14 pages, 312 KiB  
Article
Calculation of Acceleration Effects Using the Zubarev Density Operator
by Georgy Prokhorov, Oleg Teryaev and Valentin Zakharov
Particles 2020, 3(1), 1-14; https://doi.org/10.3390/particles3010001 - 3 Jan 2020
Cited by 9 | Viewed by 2536
Abstract
The relativistic form of the Zubarev density operator can be used to study quantum effects associated with acceleration of the medium. In particular, it was recently shown that the calculation of perturbative corrections in acceleration based on the Zubarev density operator makes it [...] Read more.
The relativistic form of the Zubarev density operator can be used to study quantum effects associated with acceleration of the medium. In particular, it was recently shown that the calculation of perturbative corrections in acceleration based on the Zubarev density operator makes it possible to show the existence of the Unruh effect. In this paper, we present the details of the calculation of quantum correlators arising in the fourth order of the perturbation theory needed to demonstrate the Unruh effect. Expressions for the quantum corrections for massive fermions are also obtained. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
30 pages, 376 KiB  
Communication
The Source Term of the Non-Equilibrium Statistical Operator
by Gerd Röpke
Particles 2019, 2(2), 309-338; https://doi.org/10.3390/particles2020020 - 6 Jun 2019
Viewed by 2857
Abstract
The method of Zubarev allows one to construct a statistical operator for the nonequilibrium. The von Neumann equation is modified introducing a source term that is considered as an infinitesimal small correction. This approach provides us with a very general and unified treatment [...] Read more.
The method of Zubarev allows one to construct a statistical operator for the nonequilibrium. The von Neumann equation is modified introducing a source term that is considered as an infinitesimal small correction. This approach provides us with a very general and unified treatment of nonequilibrium processes. Considering as an example the electrical conductivity, we discuss the modification of the von Neumann equation to describe a stationary nonequilibrium process. The Zubarev approach has to be generalized to open quantum systems. The interaction of the system with the irrelevant degrees of freedom of the bath is globally described by the von Neumann equation with a finite source term. This is interpreted as a relaxation process to an appropriate relevant statistical operator. As an alternative, a quantum master equation can be worked out where the coupling to the bath is described by a dissipator. The production of entropy is analyzed. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
20 pages, 993 KiB  
Article
Anomaly-Induced Transport Phenomena from Imaginary-Time Formalism
by Masaru Hongo and Yoshimasa Hidaka
Particles 2019, 2(2), 261-280; https://doi.org/10.3390/particles2020018 - 16 May 2019
Cited by 11 | Viewed by 3286
Abstract
A derivation of anomaly-induced transport phenomena—the chiral magnetic/vortical effect—is revisited based on the imaginary-time formalism of quantum field theory. Considering the simplest anomalous system composed of a single Weyl fermion, we provide two derivations: perturbative (one-loop) evaluation of the anomalous transport coefficient, and [...] Read more.
A derivation of anomaly-induced transport phenomena—the chiral magnetic/vortical effect—is revisited based on the imaginary-time formalism of quantum field theory. Considering the simplest anomalous system composed of a single Weyl fermion, we provide two derivations: perturbative (one-loop) evaluation of the anomalous transport coefficient, and the anomaly matching for the local thermodynamic functional. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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Graphical abstract

19 pages, 497 KiB  
Article
Application of the Non-Equilibrium Statistical Operator Method to the Dynamical Conductivity of Metallic and Classical Plasmas
by Mikhail Veysman, Gerd Röpke and Heidi Reinholz
Particles 2019, 2(2), 242-260; https://doi.org/10.3390/particles2020017 - 7 May 2019
Cited by 1 | Viewed by 2753
Abstract
The fruitfulness of the method of a non-equilibrium statistical operator (NSO) and generalized linear response theory is demonstrated calculating the permittivity, dynamical conductivity, absorption coefficient, and dynamical collision frequency of plasmas in the degenerate, metallic state as well as classical plasmas. A wide [...] Read more.
The fruitfulness of the method of a non-equilibrium statistical operator (NSO) and generalized linear response theory is demonstrated calculating the permittivity, dynamical conductivity, absorption coefficient, and dynamical collision frequency of plasmas in the degenerate, metallic state as well as classical plasmas. A wide range of plasma parameters is considered, and a wide range of frequencies of laser radiation acting on such plasmas is treated. New analytical expressions for the plasma response are obtained by this method, and several limiting cases are discussed. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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Graphical abstract

11 pages, 580 KiB  
Communication
Bose-Einstein Condensation from the QCD Boltzmann Equation
by Brent Harrison and Andre Peshier
Particles 2019, 2(2), 231-241; https://doi.org/10.3390/particles2020016 - 22 Apr 2019
Cited by 4 | Viewed by 3340
Abstract
We present a novel numerical scheme to solve the QCD Boltzmann equation in the soft scattering approximation, for the quenched limit of QCD. Using this we can readily investigate the evolution of spatially homogeneous systems of gluons distributed isotropically in momentum space. We [...] Read more.
We present a novel numerical scheme to solve the QCD Boltzmann equation in the soft scattering approximation, for the quenched limit of QCD. Using this we can readily investigate the evolution of spatially homogeneous systems of gluons distributed isotropically in momentum space. We numerically confirm that for so-called “overpopulated” initial conditions, a (transient) Bose-Einstein condensate could emerge in a finite time. Going beyond existing results, we analyze the formation dynamics of this condensate. The scheme is extended to systems with cylindrically symmetric momentum distributions, in order to investigate the effects of anisotropy. In particular, we compare the rates at which isotropization and equilibration occur. We also compare our results from the soft scattering scheme to the relaxation time approximation. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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23 pages, 3944 KiB  
Article
Nonperturbative Kinetic Description of Electron-Hole Excitations in Graphene in a Time Dependent Electric Field of Arbitrary Polarization
by Stanislav A. Smolyansky, Anatolii D. Panferov, David B. Blaschke and Narine T. Gevorgyan
Particles 2019, 2(2), 208-230; https://doi.org/10.3390/particles2020015 - 16 Apr 2019
Cited by 9 | Viewed by 3670
Abstract
On the basis of the well-known kinetic description of e − e + vacuum pair creation in strong electromagnetic fields in D = 3 + 1 QED we construct a nonperturbative kinetic approach to electron-hole excitations in graphene under the action of strong, [...] Read more.
On the basis of the well-known kinetic description of e − e + vacuum pair creation in strong electromagnetic fields in D = 3 + 1 QED we construct a nonperturbative kinetic approach to electron-hole excitations in graphene under the action of strong, time-dependent electric fields. We start from the simplest model of low-energy excitations around the Dirac points in the Brillouin zone. The corresponding kinetic equations are analyzed by nonperturbative analytical and numerical methods that allow to avoid difficulties characteristic for the perturbation theory. We consider different models for external fields acting in both, one and two dimensions. In the latter case we discuss the nonlinear interaction of the orthogonal currents in graphene which plays the role of an active nonlinear medium. In particular, this allows to govern the current in one direction by means of the electric field acting in the orthogonal direction. Investigating the polarization current we detected the existence of high frequency damped oscillations in a constant external electric field. When the electric field is abruptly turned off residual inertial oscillations of the polarization current are obtained. Further nonlinear effects are discussed. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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11 pages, 264 KiB  
Article
Reworking Zubarev’s Approach to Nonequilibrium Quantum Statistical Mechanics
by Francesco Becattini, Matteo Buzzegoli and Eduardo Grossi
Particles 2019, 2(2), 197-207; https://doi.org/10.3390/particles2020014 - 8 Apr 2019
Cited by 49 | Viewed by 3570
Abstract
In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially [...] Read more.
In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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14 pages, 2660 KiB  
Article
Kinetic Approach to Pair Production in Strong Fields—Two Lessons for Applications to Heavy-Ion Collisions
by David B. Blaschke, Lukasz Juchnowski and Andreas Otto
Particles 2019, 2(2), 166-179; https://doi.org/10.3390/particles2020012 - 1 Apr 2019
Cited by 8 | Viewed by 3021
Abstract
The kinetic-equation approach to particle production in strong, time-dependent external fields is revisited and three limiting cases are discussed for different field patterns: the Sauter pulse, a harmonic pulse with a Gaussian envelope, and a Poisson-distributed stochastic field. It is shown that for [...] Read more.
The kinetic-equation approach to particle production in strong, time-dependent external fields is revisited and three limiting cases are discussed for different field patterns: the Sauter pulse, a harmonic pulse with a Gaussian envelope, and a Poisson-distributed stochastic field. It is shown that for transient subcritical electric fields E ( t ) a finite residual particle number density n ( ∞ ) would be absent if the field-dependence of the dynamical phase in the Schwinger source term would be neglected. In this case the distribution function of created particles follows the law f ( t ) ∼ E 2 ( t ) . Two lessons for particle production in heavy-ion collisions are derived from this exercise. First: the shorter the (Sauter-type) pulse, the higher the residual density of produced particles. Second: although the Schwinger process in a string-type field produces a non-thermal particle spectrum, a Poissonian distribution of the (fluctuating) strings produces a thermal spectrum with an apparent temperature that coincides with the Hawking–Unruh temperature for the mean value of the string tension. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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Graphical abstract

17 pages, 1459 KiB  
Article
Generalizing Bogoliubov–Zubarev Theorem to Account for Pressure Fluctuations: Application to Relativistic Gas
by Yuri G. Rudoy and Yuri P. Rybakov
Particles 2019, 2(1), 150-165; https://doi.org/10.3390/particles2010011 - 21 Mar 2019
Viewed by 2344
Abstract
The problem of pressure fluctuations in the thermal equilibrium state of some objects is discussed, its solution being suggested via generalizing the Bogoliubov–Zubarev theorem. This theorem relates the thermodynamic pressure with the Hamilton function and its derivatives describing the object in question. It [...] Read more.
The problem of pressure fluctuations in the thermal equilibrium state of some objects is discussed, its solution being suggested via generalizing the Bogoliubov–Zubarev theorem. This theorem relates the thermodynamic pressure with the Hamilton function and its derivatives describing the object in question. It is shown that unlike to other thermodynamic quantities (e.g., the energy or the volume) the pressure fluctuations are described not only by a purely thermodynamic quantity (namely, the corresponding thermodynamic susceptibility) but also by some non-thermodynamic quantities. The attempt is made to apply these results to the relativistic ideal gases, with some numerical results being valid for the limiting ultra-relativistic or high-temperature case. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
10 pages, 539 KiB  
Communication
Low-Momentum Pion Enhancement from Schematic Hadronization of a Gluon-Saturated Initial State
by Elizaveta Nazarova, Łukasz Juchnowski, David Blaschke and Tobias Fischer
Particles 2019, 2(1), 140-149; https://doi.org/10.3390/particles2010010 - 11 Mar 2019
Cited by 4 | Viewed by 2967
Abstract
We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is [...] Read more.
We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is shown that the overpopulation of the gluon phase space in the initial state leads to an intermediate stage of Bose enhancement in the low-momentum gluon sector which due to the gluon-pion conversion process is then reflected in the final distribution function of pions. This pattern is very similar to the experimental finding of a low-momentum pion enhancement in the ALICE experiment at the CERN Large Hadron Collider (LHC). Relations to the thermal statistical model of hadron production and the phenomenon of thermal and chemical freeze-out are discussed in this context. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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11 pages, 289 KiB  
Article
Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium ϕ3 QFT
by Ivan Dadić and Dubravko Klabučar
Particles 2019, 2(1), 92-102; https://doi.org/10.3390/particles2010008 - 18 Jan 2019
Cited by 4 | Viewed by 3301
Abstract
Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and [...] Read more.
Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g ϕ 3 QFT, by using the retarded/advanced ( R / A ) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We “repair” them, while keeping d < 4 , to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Σ F ( p 0 ) does not vanish when | p 0 | → ∞ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object G F ( p 0 ) Σ F ( p 0 ) . In the FTP approach, after repairing the vertices, the corresponding composite objects are G R ( p 0 ) Σ R ( p 0 ) and Σ A ( p 0 ) G A ( p 0 ) . In the limit d → 4 , one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition ⟨ 0 | ϕ | 0 ⟩ = 0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit t → ∞ . Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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13 pages, 257 KiB  
Article
Unification of Thermo Field Kinetic and Hydrodynamics Approaches in the Theory of Dense Quantum–Field Systems
by Mykhailo Tokarchuk and Petro Hlushak
Particles 2019, 2(1), 1-13; https://doi.org/10.3390/particles2010001 - 21 Dec 2018
Cited by 1 | Viewed by 2841
Abstract
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. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
9 pages, 1203 KiB  
Article
NA61/SHINE Experiment—Program beyond 2020
by Ludwik Turko
Particles 2018, 1(1), 296-304; https://doi.org/10.3390/particles1010024 - 30 Nov 2018
Cited by 1 | Viewed by 3572
Abstract
The fixed-target NA61/SHINE experiment (SPS CERN) looks for the critical point (CP) of strongly interacting matter and the properties of the onset of deconfinement. It is a scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus, and nucleus–nucleus interactions as a [...] Read more.
The fixed-target NA61/SHINE experiment (SPS CERN) looks for the critical point (CP) of strongly interacting matter and the properties of the onset of deconfinement. It is a scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus, and nucleus–nucleus interactions as a function of collision energy and system size. This gives unique possibilities to researching critical properties of the dense hot hadronic matter created in the collision process. New measurements and their objectives, related to the third stage of the experiment after 2020, are presented and discussed here. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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11 pages, 249 KiB  
Article
Energy Conservation and the Correlation Quasi-Temperature in Open Quantum Dynamics
by Vladimir Morozov and Vasyl’ Ignatyuk
Particles 2018, 1(1), 285-295; https://doi.org/10.3390/particles1010023 - 30 Nov 2018
Cited by 3 | Viewed by 2391
Abstract
The master equation for an open quantum system is derived in the weak-coupling approximation when the additional dynamical variable—the mean interaction energy—is included into the generic relevant statistical operator. This master equation is nonlocal in time and involves the “quasi-temperature”, which is a [...] Read more.
The master equation for an open quantum system is derived in the weak-coupling approximation when the additional dynamical variable—the mean interaction energy—is included into the generic relevant statistical operator. This master equation is nonlocal in time and involves the “quasi-temperature”, which is a non- equilibrium state parameter conjugated thermodynamically to the mean interaction energy of the composite system. The evolution equation for the quasi-temperature is derived using the energy conservation law. Thus long-living dynamical correlations, which are associated with this conservation law and play an important role in transition to the Markovian regime and subsequent equilibration of the system, are properly taken into account. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
11 pages, 307 KiB  
Article
Relativistic Dissipative Fluid Dynamics from the Non-Equilibrium Statistical Operator
by Arus Harutyunyan, Armen Sedrakian and Dirk H. Rischke
Particles 2018, 1(1), 155-165; https://doi.org/10.3390/particles1010011 - 21 Jun 2018
Cited by 13 | Viewed by 3239
Abstract
We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev’s formalism for the non-equilibrium statistical operator. In particular, we discuss the shear-stress tensor to second order in gradients and argue that the relaxation terms for the dissipative [...] Read more.
We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev’s formalism for the non-equilibrium statistical operator. In particular, we discuss the shear-stress tensor to second order in gradients and argue that the relaxation terms for the dissipative quantities arise from memory effects contained in the statistical operator. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing Kubo-type formulae for the second-order transport coefficients. Full article
(This article belongs to the Special Issue Nonequilibrium Phenomena in Strongly Correlated Systems)
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