Related papers: Functionals and the Quantum Master Equation
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The general solution to the quantum master equation (and its $Sp(2)$ symmetric counterpart) is constructed explicitly in case of finite number of variables. It is shown that the finite-dimensional solution is physically trivial and thus can…
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra. For a compact manifold, a…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path…
Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being…
This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.
A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…