1,721,072 research outputs found
K.R. Parthasarathy’s contributions to quantum Gaussian distributions and applications
No full textIn the “short pedagogical essay” [1], published in 2010, K.R. Parthasarathy illustrated the notion of a quantum Gaussian state as a natural extension of the idea of Gaussian or normal distribution in classical probability. This presentation led to some interesting open problems on symmetry transformation and other properties of quantum Gaussian states, calling for further investigation which he continued in the following years
Quantum Fokker-Planck models: an Open System Approach
No full textWe start with a short introduction to quantum master equations
for semigroups of completely positive normal maps describing
the evolution of open quantum systems and discuss in, particular,
the structure of generators (Gorini-Kossakowski-Sudarshan-Lindblad).
We study the quantum Fokker--Planck equation for the density matrix
of a quantum state with the approach developed for the study of master equations in open quantum systems. We discuss existence of stationary states and long time asymptotics
Quantum Markov Semigroups and Flows Arising from Form Generators on B(h)
No full textWe present the construction of completely positive semigroups on
the von Neumann algebra B(h) of all bounded operators on a complex
separable Hilbert space h with a given form generator and their
dilations to homomorphic inner flows via Hudson-Parthasarathy
quantum stochastic differential equations. We discuss
concrete examples emphasizing non conservativity issues
of the minimal semigroup that could end up in a type II
product system of the minimal dilation
Two-photon absorption and emission process
No full textWe analyze the two-photon absorption and emission process and characterize the stationary states at zero and positive temperature. We show that entangled stationary states exist only at zero temperature and, at positive temperature, there exists infinitely many
commuting invariant states satisfying the detailed balance condition
Decomposition and Classificationof Generic Quantum MarkovSemigroups: The Gaussian Gauge Invariant Case
No full textWe study the structure of generic quantum Markov semigroups, arising from the stochastic limit of a discrete system with generic Hamiltonian interacting with a Gaussian gauge invariant reservoir. We show that they can be essentially written as the sum of their irreducible components determined by closed classes of states of the associated classical Markov jump process. Each irreducible component turns out to be recurrent, transient or have an invariant state if and only if its classical (diagonal) restriction is recurrent, transient or has an invariant state, respectively. We classify invariant states and study
convergence towards invariant states as time goes to infinity
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