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The governing theory of electric signal transfer through nerve fibre, as established by Hodgkin and Huxley in the 1950s, uses for the description of action potential a clever combination of various concepts of electrochemistry and circuit theory; however, this theory neglects some fundamental features of charge transport through any conductor, e.g., the existence of a temporary charged layer on its boundary accompanied by an external electric field. The consequences of this fact are, among others, the introduction of a non-adequate concept of “conduction velocity” and the obscure idea of saltatory propagation of action potential in myelinaed nerve fibres. Our approach, based on standard transport theory and, particularly, on the submarine cable model, describes the movement of the front of the action potential as a diffusion process characterized by the diffusion constant DE. This process is physically realized by the redistribution of ions in the nervous fluid (axoplasm), which is controlled by another diffusion constant DΩ ≪ DE. Since the action bound with the movement of Na+ and K+ cations prevailing in the axoplasm is comparable with the Planck constant ℏ (i.e. DΩ → ℏ∕2M, where M is ion mass), signal transfer is actually a quantum process. This fact accounts for the astonishing universality of the transfer of action potential, which is proper to quite different species of animals. As is further shown, the observed diversity in the behaviour of nerve tissues is controlled by the scaling factor $$\sqrt{(D_{\Omega} / D_E)}$$ , where DΩ is of a quantum nature and DE of an essentially geometric one.

Presented is a brief overview of recent developments of topics addressed by the reviews and original papers of this volume related to non-equilibrium phenomena in various (especially mesoscopic) systems and the foundations of quantum physics.

This text presents a brief overview of the recent development of topics addressed by the original papers of this volume related to non-equilibrium phenomena in various (especially mesoscopic) systems and the foundations of quantum physics. A selection of relevant literature is included.

Transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island are calculated. The island is represented by an Anderson type local center. The tunneling spectral functions simulate nickel. Transient magnetic currents under a constant galvanic bias between the electrodes are invoked by sudden switching of the junctions. The process is treated numerically using the non-equilibrium Greens functions (NEGF) (Kalvova et al., J. Supercon. Novel Mag. 26, 773, 2013, J. Supercon. Novel Mag. 28, 1087, 2015) from the early stages of the transient depending on the finite time initial conditions to the late asymptotics of free relaxation to the steady state. This serves as a reference for testing the simpler and physically transparent description by a generalized master equation, resulting from the NEGF scheme approximated by the Generalized Kadanoff-Baym Ansatz (GKBA) (Spicka et al., Internat. J. Mod. Phys. 28 1430013-1, 2014). It turns out that decisive for the applicability of GKBA is the spectral structure of tunneling functions and their positioning with respect to the island level dependent on the bias and the exchange splitting. Favorable for the validity of GKBA are weak tunneling and spectrally flat tunneling functions. Stretching of these conditions toward the realistic situation for transition metal electrodes with their complex sd surface-modified spectral properties is limited.

This paper summarizes the recent state of the art of the following topics presented at the FQMT’08 conference: Foundations of quantum physics, Quantum measurement; Quantum noise, decoherence and dephasing; Cold atoms and Bose–Einstein condensation; Physics of quantum computing and information; Nonequilibrium quantum statistical mechanics; Quantum, mesoscopic and partly classical thermodynamics; Mesoscopic, nano-electro-mechanical systems and optomechanical systems; Spins systems and their dynamics, Brownian motion and molecular motors; Physics of biological systems, and Relevant experiments from the nanoscale to the macroscale. To all these subjects an introduction is given and the recent literature is overviewed. The paper contains some 680 references in total.

Recent developments in technologies and experiments enable us to observe dynamical behavior of very small quantum systems under conditions when it is sensitive to system parameters, internal interactions, the environment and the external time-dependent fields. This contribution deals with the status and perspectives of description of such truly non-equilibrium quantum many body systems using the non-equilibrium Green's functions (NGF). The basic aim of this approach is to describe time development of the many-body system out of equilibrium from its initial state over its transient dynamics to its long time asymptotic evolution. The early stages of the transient evolution will be characterized for a broad class of the initial conditions generated in the course of Keldysh switch-on states. Gradual loss of initial correlations due to interactions and related renormalization processes in the system may, under favorable conditions, give rise to the evolution stage expressible in terms of non-equilibrium quasi-particles. This permits to reduce the description of the system behavior to a quantum transport equation. The consistency of such approximations for NGF may be judged by checking the non-equilibrium version of transport Ward identities. These identities follow from the gauge invariance of the 1st kind for NGF. To cover the whole time domain of the transient, we obtain the non-equilibrium Ward identities for NGF with initial conditions included.

The Non-Equilibrium Fluctuation-Dissipation Theorem (NE FDT) is formulated within the Non-Equilibrium Green Function (NEGF) formalism. The relation of this theorem to a simplified kinetic theory of non-equilibrium dynamics of electrons in open quantum systems is discussed. The possibility of such a simplified description is first discussed on non-equilibrium dynamics of the molecular bridge model represented by calculations of transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island of an Anderson local center type. This model can be treated by using the full set of equations for NEGF, which can be solved numerically. This provides a reference framework for testing the possibility of a simpler and physically more transparent solution based on a Non-Markovian Generalized Master Equation (GME) as an approximation of the full set of NEGF equations. The advantages and limitations of the use of the Generalized Kadanoff-Baym Ansatz (GKBA) for this simplified description is demonstrated. The basic question is the range of applicability of this approximation. It turns out that for our specific model the decisive feature is the spectral structure of the tunneling functions of both electrodes and their positioning with respect to the island level depending on the bias and the exchange splitting. Finally, the relation of this simplified description to non-equilibrium generalization of FDT is shown independently on the chosen model. The connection between the NEGF reconstruction equations and the non-equilibrium version of FDT is introduced and the possible approximations of this general scheme are discussed.

Virial corrections to the Boltzmann equation for quasiparticles are obtained from non-equilibrium Green's functions. These corrections are expressed in terms of shifts in space and time that characterize non-locality of scattering integrals. The space shifts parallel finite-diameter corrections to collisions of hard spheres. The time shift is identified as the collision delay. All shifts are given by derivatives of the phase shift in a binary collision.

This paper deals with the recent state of the art of the following topics presented at the FQMT’11 conference: foundations of quantum physics, quantum measurement; nonequilibrium quantum statistical physics; quantum thermodynamics; quantum measurement, entanglement and coherence; dissipation, dephasing, noise, and decoherence; quantum optics; macroscopic quantum behavior; e.g. cold atoms; Bose-Einstein condensates; physics of quantum computing and quantum information; mesoscopic, nano-electro-mechanical systems and nano-optical systems; spin systems and their dynamics; biological systems and molecular motors; and cosmology, gravitation and astrophysics. The lectures and discussions at the FQMT’11 conference, as well as the contributions to the relatedtopical issue, reveal important themes for future development. The recent literature is included.

The quasiparticle approximation and corrections beyond it are derived from expansion in the spirit of the virial corrections. This way, the Boltzmann equation for electrons in semiconductors is recovered from the nonequilibrium Green's functions without unjustified neglect of the former theory. The present approach gives higher-order contributions to the scattering rates and provides observables as functionals of the quasiparticle distribution. The application scheme is of the same simplicity as the one based on the quasiparticle approximation. Five applications to phenomena beyond the scope of the quasiparticle approximation are presented: two-phonon scattering rates, compensation of wave-function remormalization for isotropic elastic scattering, quasiparticle backflow, backflow current of waves, and discussion of the collisional broadening.

This paper investigates the question whether a realistic black hole can be in principal similar to a star, having a large but finite redshift at its horizon. If matter spreads throughout the interior of a supermassive black hole with mass $M\sim10^9M_\odot$, it has an average density comparable to air and it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field describing H atoms is coupled to the curvature scalar with dimensionless coupling $\xi$. In the Bose-Einstein condensed groundstate an exact, self-consistent solution for the metric occurs for a certain large value of $\xi$, quadratic in the black hole mass. It is put forward that $\xi$ is set by proper choice of the background metric as a first step of a renormalization approach, while otherwise the non-linearities are small. The black hole has a hair, the binding energy. Fluctuations about the ground state are considered., Comment: 18 pages Latex Physica E style

A nonequilibrium Ward identity (NE WI) connecting the scalar transport vertex correction with one-particle self-energy is derived using the global $\mathrm{U}(1)$ symmetry of the fermion nonequilibrium Green's functions (NGF). The nonperturbative derivation does not depend on the details of the many-body system. A renormalized multiplicative composition rule for the NGF, reflecting time coherence, is obtained and related to the NE WI. Applications involve (i) testing the consistency of approximations shown in the example of a self-consistent Born approximation for disorder scattering, and (ii) in the general quantum transport theory, the formalism permits one to assess routes to generalized master equations, in particular those based on the generalized Kadanoff-Baym ansatz.

The characteristic time of formation of correlations at high temperature limit is given by the inverse plasma frequency \( \tau _C \approx \frac{1} {{\omega _p }} = \frac{{\sqrt 2 }} {{\upsilon _{th} \kappa }} \) . The inverse plasma frequency indicates that the dominant role play the long range fluctuation. On the other hand, we also see that the correlation time is found to be given by the time a particle needs to travel through the range of the potential with a thermal velocity υth. This confirms the numerical finding of [12] that the correlation or memory time is proportional to the range of interaction. In the low temperature region, i.e., in highly degenerated system μ 》 T one finds a differentpicture. From (3) we can calculate the formationofcorrelationsaswell. 13,14 Unlike in the classical case, the equilibrium limit of the degenerated case is rapidly built up and then oscillates around the equilibrium value. We can define the build up time τ C as the time where the correlation energy reaches its first maximum, \( \tau _C = 1.0\frac{\hbar } {\mu } \) . Note that τ C is in agreement with the quasiparticle formation time known as Landau’s criterion for is the Fermi energy. Indeed, the quasiparticle formation and the build up of correlations are two alternative views of the same phenomena. The formation of binary correlations is very fast on the time scale of dissipative process. Under extremely fast external perturbations, like the massive femto second laser pulses, the dynamics of binary correlations will hopefully become experimentally accessible. Even if related measurement will not reveal any unexpected features, the experimental justification of basic concepts of the non-equilibrium many-body physics is very desirable.

The short time behavior of a disturbed system is influenced by off-shell motion and best characterized by the reduced density matrix possessing high energetic tails. We present analytically the formation of correlations due to collisions in an interacting Fermionic system with and without initial correlation. After this short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in the thermodynamical limit., Comment: Proceedings KB99 Workshop, September 20-24 1999, Rostock, Germany

For a set of realistic nucleon-nucleon potentials we evaluate microscopic parameters of binary collisions: a time duration of the scattering state, a mean distance and a rotation of nucleons during a collision. These parameters enter the kinetic equation as non-instantaneous and non-local corrections of the scattering integral, i.e., they can be experimentally tested. Being proportional to off-shell derivatives of the scattering T-matrix, non-instantaneous and non-local corrections make it possible to compare the off-shell behavior of different potentials in a vicinity of the energy shell. The Bonn one-Boson-exchange (A-C) and Paris potentials are found to yield very close results, while the separable Paris potential differs., Comment: Phys. Rev. C sub

Within quantum molecular dynamics (QMD) simulations we demonstrate the effect of virial corrections on heavy ion reactions. Unlike in standard codes, the binary collisions are treated as nonlocal so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values. Complementary Boltzmann-Uehling-Uhlenbeck simulations reveal that the nonlocality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced preequilibrium emission of particles.

We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data. The effect of the off-shell motion and the non-local and non-instant collisions on the dynamics of the system can be characterised in terms of thermodynamic functions such as the energy density or the pressure tensor. Non-equilibrium counterparts of these functions and the corresponding balance equations are derived and discussed from two points of view. Firstly, they are used to prove the conservation laws. Secondly, the role of individual microscopic mechanisms in fluxes of particles and momenta and in transformations of the energy is clarified., Comment: Book

The nonlocal scattering-in and scattering-out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the scattering-in and -out processes are conjugated by the space and time inversions. Generalizations of the Enskog equation to Fermi liquid systems are hindered by the need for particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can be fulfilled simultaneously only for the Bruckner type of internal Pauli blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of bosons.

The kinetic theory recently implemented in heavy ion reactions combines a non-local and non-instant picture of binary collisions with quasiparticle features. We show that the non-instant description is compatible with the spectral concept of quasiparticles while the commonly used variational concept is consistent only with instant collisions. The rearrangement energy, by which the variational concept surpasses the spectral one, is shown to be covered by a medium effect on non-instant collisions.