Brownian particle in ideal gas: explicit density expansions, conditional probabilities, and amusing properties of molecular chaos

Explicit density expansions of non-equilibrium probability distribution functions for molecular Brownian particle in ideal gas are obtained in original form what visually implies (is exact solution to) the previously established dynamical virial relations. Role of these relations in unbiased analysis of molecular chaos properties in many-particle statistical mechanics, including the mobility 1/f noise, is newly investigated in clear terms of conditional probabilities and averages.Comment: 11 pages, no figures, LaTeX2e revtex4-

Quantum generalized fluctuation-dissipation relations in terms of time-distributed observations

New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in quantum system turns any measurement in it to a source of its extra perturbations, and because of this effect relations between probabilities of mutually time-reversed processes become definitely non-local in their functional spaceComment: 15 pages, no figures, LaTeX2e iopar

Thermodynamic restrictions on statistics of molecular random walks

It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular Brownian particle in a fluid. This expansion leads to inequality connecting logarithmic derivative of the distribution with respect to fluid density and characteristic volume occupied by pair statistical correlation between the path and fluid molecules. Due to the inequality, finiteness of this volume means that asymptotic of the distribution is essentially non-Gaussian. For principal case when fluid is dilute gas it is demonstrated that the pair correlation volume is actually finite and bounded above. Therefore even under the Boltzmann-Grad limit the path distribution possess power-law long tails (cut off at distances of ballistic flight).Comment: 13 pages, no figures, LaTex svjour2, submitted to JS

A simple model for thermomagnetic instability of critical state dynamics in superconductive films

An one-dimensional model of magnetic flux penetration into thin strip-like superconductive film is subject to numerical analysis which combines explicit account for specific oblate geometry of magnetic field lines around the film and a simplest phenomenology of the flux flow resistance under rigid pinning of vortices with temperature-dependent critical current.Comment: 6 pages, 10 figures, RevTex4, extended version of poster presented to Int. Conference on Low Temperature Physics in Kharkov, Ukraine, June 200

Reconstruction of plane circular currents from their orthogonal magnetic field

The solution is presented to the problem what distribution of electric current in thin circular film provides a given distribution of normal (perpendicular to ilm) component of the current-induced magnetic field at film's surface.Comment: 4 pages, 1 figure, RevTex

Quantum Brownian motion and a theorem on fundamental 1/f noise

We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures irreversible behavior of the dynamical subsystem, that is finite diffusivities of its coordinates in thermodynamically equilibrium state and finite drift velocities and mobilities in non-equilibrium steady state in presence of external driving forces. It is shown that, nevertheless, regardless of characteristics of the interaction, the diffusivity and mobility have no certain values but instead vary from one observation to another and undergo 1/f-type or flicker-type low-frequency fluctuations.Comment: 10 pages, no figures, latex2e iopar

On 1/f-noise of electron in phonon field

Exact propagator of density matrix of particle (electron) under influence of thermal vibrations of its medium (phonons) is treated in simplest approximation beyond the Fermi's golden rule. It is shown that uncertainties \,\sim\h/t\, in energy exchanges with the medium give rise to flicker fluctuations in rate of diffusion (diffusivity) of the particleComment: 5 pages, no figures, Latex2e, submitted to "Pis'ma v ZhETF" (JETP Letters); original Russian text is attached to the source text fil

Exercises in simplest dynamical random walk, or Quantum path integral approach to true diffusion law and 1/f noise of classical particle interacting with ideal gas

Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is demostrated between results of an naturally arising simple approximation of this integral and results obtained by formally different methods, thus in a new fashion showing inevitability of scaleless 1/f-type fluctuations in rates of molecular Brownian motions and other dynamical transport and evolution processes.Comment: 23 pages, no figures, LaTeX2e elsart3

Once again on molecular Brownian motion and related fundamental 1/f noise: a logical analysis of exact equations

The paper contains a simple semi-quantitative analysis of a structure of solution to the exact Bogolyubov functional equation for a particle interacting with ideal gas and driven by an external force, in comparison with solutions to model kinetic equations for the same system. It is shown that the exact equation inevitably predicts existence of significant 1/f-type fluctuations in mobility of the particle, and this result directly extends to particles in arbitrary fluid.Comment: 16 pages, no figures, LaTeX iopar

On energy exchange rate and entropy production operators in quantum fluctuation-dissipation relations

For quantum systems with externally time-varied Hamiltonians a definition of operators of system's energy change rate (work per unit time) and entropy production observables is suggested and discussed in the context of rigorous statistical equalities (generalized fluctuation-dissipation relations) under the Jordan-symmetrized chronological operator ordering rule.Comment: 10 pages, no figures, LaTeX2e iopar