A Schroedinger link between non-equilibrium thermodynamics and Fisher information

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis.Comment: 12 pages, no figure

Kolmogorov-Burgers Model for Star Forming Turbulence

The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range it behaves as Burgers turbulence developing shock singularities. On the base of the She-Leveque analytical model we then predict the velocity power spectrum in the inertial range to be E_k ~ k^{-1.74}. This result reproduces the observational Larson law, ~ l^{0.74...0.76}, [Larson, MNRAS 194 (1981) 809] and agrees well with recent numerical findings by Padoan and Nordlund [astro-ph/0011465]. The application of the model to more general dissipative structures, with higher fractal dimensionality, leads to better agreement with recent observational results.Comment: revised, new material added, 8 page

Quantum Belief Propagation

We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these systems at non-zero temperature, decaying on a length scale inversely proportional to the temperature. We compare to exact results on a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a relative error of less than $10^{-5}$, while more elaborate calculations further reduce the error.Comment: 4 pages, 1 figure; revised time estimates due to improved implementation. Typographical corrections to Eq. 7 made; thanks to David Poulin for pointing out the mistak

Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states

We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to the ferromagnetic electrodes and/or spin polarization of the tunnel junction. We set up a second quantization scheme for density operators in the Liouville-Fock space constructing causal field superoperators using the fundamental physical principles of causality/probability conservation and the fermion-parity superselection (univalence). The time-dependent perturbation series for the time-evolution is renormalized by explicitly performing the wide-band limit on the superoperator level. The short and long-time reservoir correlations are shown to be tightly linked to the occurrence of causal field destruction and creation superoperators, respectively. The effective theory takes as a reference a damped local system, providing an interesting starting point for numerical calculations of memory kernels in real-time. A remarkable feature of this approach is the natural appearance of a measurable fermion-parity protected decay mode. It already can be calculated exactly in the Markovian, infinite temperature limit by leading order perturbation theory, yet persists unaltered for the finite temperature, interaction and tunneling spin polarization. Furthermore, we show how a Liouville-space analog of the Pauli principle directly leads to the exact result in the noninteracting limit: surprisingly, it is obtained in finite (second) order renormalized perturbation theory, both for the self-energy as well as the time-evolution propagator. For this limit we calculate the time-evolution of the full density operator starting from an arbitrary initial state on the quantum dot, including spin and pairing coherences and two-particle correlations.Comment: This version contains the more extensive introduction and the conclusion, discussing an experimental relevance of the obtained exact result for the new decay mode. A lot of new references have been added. The more detailed comparison of the results obtained for the noninteracting case with the known results has been done. Small typos have been fixe

Casimir energy for spherical shell in Schwarzchild black hole background

In this paper, we consider the Casimir energy of massless scalar field which satisfy Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.Comment: 10 pages, no figure,discussion added, references added, has been accepted for the publication in GR