Search results for " 47N50"

showing 2 items of 2 documents

Instability of Equilibrium States for Coupled Heat Reservoirs at Different Temperatures

2007

Abstract We consider quantum systems consisting of a “small” system coupled to two reservoirs (called open systems). We show that such systems have no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the product of the temperatures are not too small. Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators (“positive temperature Hamiltonians”) which generate the dynamics of the systems under consideration.

Non-equilibrium quantum theoryQuantum dynamicsLiouville operators82C10; 47N50FOS: Physical sciencesFeshbach mapQuantum phasesSpectral deformation theory01 natural sciencesOpen quantum systemQuantum mechanics0103 physical sciencesQuantum operationStatistical physics0101 mathematicsQuantum statistical mechanicsMathematical PhysicsMathematicsQuantum discord82C10010102 general mathematicsMathematical Physics (math-ph)Quantum dynamical systemsQuantum process47N50010307 mathematical physicsQuantum dissipationAnalysis
researchProduct

Quantum graphs with mixed dynamics: the transport/diffusion case

2013

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.

Statistics and ProbabilityPhysicsPartial differential equationSemigroupMathematical analysis34B45 47D06 47N50Hilbert spaceFOS: Physical sciencesGeneral Physics and AstronomyBoundary (topology)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)System of linear equationssymbols.namesakeMathematics - Analysis of PDEsModeling and SimulationQuantum graphFOS: MathematicssymbolsDiffusion (business)Transport phenomenaMathematical PhysicsAnalysis of PDEs (math.AP)
researchProduct