We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The represen...We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.展开更多
We report on a new derivation of the extended Feynman propagator for the harmonic oscil-lator at and beyond caustics using the explicit eigenfunction expansion for the propagator.It is shown that the Maslov correction...We report on a new derivation of the extended Feynman propagator for the harmonic oscil-lator at and beyond caustics using the explicit eigenfunction expansion for the propagator.It is shown that the Maslov corrections beyond caustics are directly determined by the parityof the eigenfunctions. The phase correction and related effect of the propagator of a chargedparticle in constant magnetic field and in the presence of Chern-Simon backgraound gaugefield are studied.展开更多
By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks ...We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
文摘We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.
文摘We report on a new derivation of the extended Feynman propagator for the harmonic oscil-lator at and beyond caustics using the explicit eigenfunction expansion for the propagator.It is shown that the Maslov corrections beyond caustics are directly determined by the parityof the eigenfunctions. The phase correction and related effect of the propagator of a chargedparticle in constant magnetic field and in the presence of Chern-Simon backgraound gaugefield are studied.
基金supported by the Special Funds of the National Natural Science Foundation of China (Grant No.10947017/A05)
文摘By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
基金supported by the National Natural Science Foundation of China (Grant No. 11174025)
文摘We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.
基金supported by an NSERC granta startup fund of University of Alberta
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
