Nonequilibrium Initial State Research Articles

Toward a Nonequilibrium Green Functions Approach to Diffusion in Strongly Coupled Finite Quantum Systems

AbstractTransport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we apply a Nonequilibrium Green Functions approach using a lattice model as a basic system. This allow us to treat a finite spatially inhomogeneous system with an arbitrary nonequilibrium initial state. Placing all particles initially to one side of the system allows for a nonequilibrium study of diffusion. Strong correlation effects are incorporated via T‐matrix selfenergies. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonequilibrium quantum fluctuations of work.

The concept of work is basic for statistical thermodynamics. To gain a fuller understanding of work and its (quantum) features, it needs to be represented as an average of a fluctuating quantity. Here I focus on the work done between two moments of time for a thermally isolated quantum system driven by a time-dependent Hamiltonian. I formulate two natural conditions needed for the fluctuating work to be physically meaningful for a system that starts its evolution from a nonequilibrium state. The existing definitions do not satisfy these conditions due to issues that are traced back to noncommutativity. I propose a definition of fluctuating work that is free of previous drawbacks and that applies for a wide class of nonequilibrium initial states. It allows the deduction of a generalized work-fluctuation theorem that applies for an arbitrary (out-of-equilibrium) initial state.

Equilibration of a finite-temperature binary Bose gas formed by population transfer

We consider an equilibrium single-species homogeneous Bose gas from which a proportion of the atoms are instantaneously and coherently transferred to a second species, thereby forming a binary Bose gas in a non-equilibrium initial state. We study the ensuing evolution towards a new equilibrium, mapping the dynamics and final equilibrium state out as a function of the population transfer and the interspecies interactions by means of classical field methods. While in certain regimes, the condensate fractions are largely unaffected by the population transfer process, in others, particularly for immiscible interactions, one or both condensate fractions are vastly reduced to a new equilibrium value.

Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb, and Pb+Pb collisions.

We determine the transverse system size of the initial nonequilibrium Glasma state and of the hydrodynamically evolving fireball as a function of produced charged particles in p+p, p+Pb, and Pb+Pb collisions at the Large Hadron Collider. Our results show features similar to those of recent measurements of Hanbury Brown-Twiss (HBT) radii by the ALICE Collaboration. Azimuthal anisotropy coefficients vn generated by combining the early time Glasma dynamics with viscous fluid dynamics in Pb+Pb collisions are in excellent agreement with experimental data for a wide range of centralities. In particular, event-by-event distributions of the vn values agree with the experimental data out to fairly peripheral centrality bins. In striking contrast, our results for p+Pb collisions significantly underestimate the magnitude and do not reproduce the centrality dependence of data for v2 and v3 coefficients. We argue that the measured vn data and HBT radii strongly constrain the shapes of initial parton distributions across system sizes that would be compatible with a flow interpretation in p+Pb collisions. Alternately, additional sources of correlations may be required to describe the systematics of long-range rapidity correlations in p+p and p+Pb collisions.

Application of the Generalized Work Relation for an N-level Quantum System

An efficient periodic operation to obtain the maximum work from a nonequilibrium initial state in an N–level quantum system is shown. Each cycle consists of a stabilization process followed by an isentropic restoration process. The instantaneous time limit can be taken in the stabilization process from the nonequilibrium initial state to a stable passive state. In the restoration process that preserves the passive state a minimum period is needed to satisfy the uncertainty relation between energy and time. An efficient quantum feedback control in a symmetric two–level quantum system connected to an energy source is proposed.

Two‐dimensional hybrid models of H+‐He++ expanding solar wind plasma heating

AbstractPreferential heating and acceleration of the solar wind He++ ions compared to protons in fast solar wind streams have been known for decades, thanks to in situ spacecraft measurements at 0.29–5 AU. Turbulent magnetic field fluctuations with approximate power law spectra have been observed as well. However, the exact causes of these processes are still not known due to the lack of detailed information on the magnetic field fluctuations and ion velocity distributions in the acceleration region of the solar wind. Here the collisionless heating processes in expanding solar wind plasma are investigated using 2‐D hybrid modeling with parameters appropriate to the heliocentric distance of 10 RS. In this study the ion dynamics is described kinetically, while electrons are treated as a background massless fluid in an expanding solar wind model. The source of free energy for the heating is introduced through an initial nonequilibrium state of the plasma with large He++ ion temperature anisotropy or with super‐Alfvénic relative ion drift. We also employ an externally imposed spectrum of magnetic fluctuations in the frequency range below the proton gyroresonant frequency to heat the He++ ions. We investigate the effects of solar wind radial expansion by modeling several values of the expansion rate in a parametric study. We find that the preferential ion heating is attained in both nonexpanding and expanding solar wind models. Thus, the expansion has little effect on the preferential He++ ion heating by the processes considered here. Moreover, the expansion leads to faster evolution of the magnetosonic drift instability, reducing the drift velocity to lower values sooner, and the corresponding generation of the magnetic fluctuations that heat the ions, compared to the nonexpanding case. This is due to the reduction of the perpendicular particle velocities in the expanding (inflated) frame. For cases with little proton perpendicular heating, the solar wind expansion leads to the reduction of the proton temperature anisotropy to values less than one in the low‐βp∥ solar wind acceleration region consistent with some observed values. However, this effect must be offset by perpendicular proton heating—likely by the same process that heats the He++ ions to be consistent with the full range of observed proton perpendicular temperature values.

Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time tw and time of observation t – tw with t > tw. We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X∞. Analysis of simulation results show that the insertion of disorder leads to new values of X∞ with X∞diluted > X∞pure.

Formation of magnetic discontinuities through viscous relaxation

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach of describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topology-preserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls.

Dynamical Casimir–Polder potentials in non-adiabatic conditions

In this paper we review different aspects of the dynamical Casimir–Polder potential between a neutral atom and a perfectly conducting plate under nonequilibrium conditions. In order to calculate the time evolution of the atom–wall Casimir–Polder potential, we solve the Heisenberg equations describing the dynamics of the coupled system using an iterative technique. Different nonequilibrium initial states are considered, such as bare and partially dressed states. The partially dressed states considered are obtained by a sudden change of a physical parameter of the atom or of its position relative to the conducting plate. Experimental feasibility of detecting the considered dynamical effects is also discussed.

Dissipative Dynamics of Two-Level Systems in Low Temperature Glasses

An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe dynamics of a central chromophore embedded in a bath of two-level systems commonly found in low-temperature glasses. By treating the Hamiltonian in the polaron frame, we can account for initial nonequilibrium bath states as well as the spatially correlated environmental effect. Relevant realistic situations are explored by adopting parameters from previous experiments. It is found that the temperature of the boson bath has a substantial effect on the population relaxation and the decoherence process, and a higher temperature also results in a higher saturation value of the entanglement entropy, while the coupling between the chromophore and the TLS has an effect that goes counter to that of the temperature.

Interaction quench in nonequilibrium Luttinger liquids

We study the relaxation dynamics of a nonequilibrium Tomonaga-Luttinger model after a sudden interaction switch-on (``quench''), focusing on a double-step initial momentum distribution function. In the framework of the nonequilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasiparticle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.

Nonequilibrium dynamics of a system with quantum frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.

Functional thermo-dynamics: A generalization of dynamic density functional theory to non-isothermal situations

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

On holographic thermalization and gravitational collapse of tachyonic scalar fields

Abstract In this paper we study the thermalization of a spatially homogeneous system in a strongly coupled CFT. The non-equilibrium initial state is created by switching on a relevant perturbation in the CFT vacuum during Δt ≳ t ≳ − Δt. Via AdS/CFT, the thermalization process corresponds to the gravitational collapse of a tachyonic scalar field (m 2 = −3) in the Poincare patch of AdS 5. In the limit $ \varDelta t<\frac{0.02 }{T} $ , the thermalization time t T is found to be quantitatively the same as that of a non-equilibrium state created by a marginal perturbation discussed in ref. [5]. In the case $ \varDelta t\gtrsim \frac{1}{T} $ we also obtain double- collapse solutions but with a non-equilibrium intermediate state at t = 0. In all the cases our results show that the system thermalizes in a typical time $ {t_T}\simeq \frac{O(1) }{T} $ . Besides, a conserved energy-moment current in the bulk is found, which helps understand the qualitative difference of the collapse process in the Poincare patch from that in global AdS [10, 11].

Few-particle quantum dynamics–comparing nonequilibrium Green functions with the generalized Kadanoff–Baym ansatz to density operator theory

The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open.Here we analyze this correspondence by studying the generalized Kadanoff–Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

Thermodynamics of projective quantum measurements

Quantum measurement of a system can change its mean energy as well as entropy. A selective measurement (classical or quantum) can be used as a ‘Maxwell's demon’ to power a single-temperature heat engine by decreasing the entropy. Quantum mechanically, so can a non-selective measurement, despite increasing the entropy of a thermal state. The maximal amount of work extractable following the measurement is given by the change in free energy: W(non-)selmax = ΔEmeas − TBathΔS(non-)selmeas. This follows from the ‘generalized 2nd law for nonequilibrium initial state’ (Hasegawa et al 2010 Phys. Lett. A 374 1001–4), an elementary reduction of which to the standard law is given here. It is shown that Wselmax − Wnon-selmax is equal to the work required for resetting the memory of the measuring device and that no such resetting is needed in the non-selective case. Consequently, a single-bath engine powered by either kind of measurement works at a net loss of TBathΔSnon-selmeas per cycle. By replacing the measurement by a reversible ‘pre-measurement’ and allowing a work source to couple to the system and memory, the cycle can be rendered completely reversible.

Loschmidt echo with a nonequilibrium initial state: Early-time scaling and enhanced decoherence

We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at $t=0$ so that its state at $t=0^+$, remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a non-equilibrium situation. This state now evolves with two Hamiltonians, the final Hamiltonian following the quench and its modified version which incorporates an additional term arising due to the coupling of the central spin to the environment. Using a generic short-time scaling of the decay rate, we establish that in the early time limit, the rate of decay of the LE (or the overlap between two states generated from the initial state evolving through two channels) close to the quantum critical point (QCP) of E is independent of the quenching. We do also study the temporal evolution of the LE and establish the presence of a crossover to a situation where the quenching becomes irrelevant. In the limit of large quench amplitude the non-equilibrium initial condition is found to result in a drastic increase in decoherence at large times, even far away from a QCP. These generic results are verified analytically as well as numerically, choosing E to be a transverse Ising chain where the transverse field is suddenly quenched.

Non-Equilibrium Critical Dynamics of Ferromagnets with Long Range Correlated Defects

The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.

Field-Theory Description of Nonequilibrium Critical Dynamics for Spin Systems

Renormalization-group approach is applied to investigate the short-time nonequilibriumcritical behavior of pure and diluted spin systems with nonmagnetic point-like impurities.The dissipative relaxation dynamics with non-conserved order parameter is considered. For thefirst time the description of the order parameter growth induced by the initial nonequilibriumstate of system is carried out at fixed dimension d = 3 without use of ε-expansion.

The impact of hierarchically constrained dynamics with a finite mean of cluster sizes on relaxation properties

In this paper, a stochastic scenario of relaxation underlying the generalization (Kahlau et al., 2010) [15] of the Cole–Davidson (CD) and Kohlrausch–Williams–Watts (KWW) functions is proposed. As it has been shown (Kahlau et al., 2010) [15], the new three-parameter time-domain fitting function provides a very flexible description of the dielectric spectroscopy data for viscous glass-forming liquids. In relation to that result we discuss a hierarchically-constrained model yielding the proposed relaxation fitting function. Within the “exponentially decaying relaxation contributions” framework we show origins of the high-frequency (short-time, respectively) fractional power law, i.e., the characteristic feature of the new, as well as, of both CD and KWW response functions. We also bring into light a reason for which their common behavior in the opposite frequency limit is linear on external field frequency. Finally, we relate the new relaxation pattern (Kahlau et al., 2010) [15] with the Generalized Gamma (GG) survival probability of an imposed, non-equilibrium initial state in a relaxing system.