Related papers: Feynman operator calculus and singular quantum osc…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
We investigate the dynamics of a classical mechanical oscillator coupled to the simplest quantum system, a single qubit. Using the Feynman-Vernon influence functional formalism, we show that the qubit's influence manifests as both…
Experimental tests of the suggestion that the generalization of Wheeler and Feynman's time symmetric system is the dynamical basis underlying quantum mechanics are considered. In a time-symmetric system, the instantaneous correlations…
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
Recently R. N. Costa Filho et al. (PRA 84, 050102(R) (2011)) have introduced a position dependent infinitesimal translation operator which corresponds to a position dependent linear momentum and consequently to a position dependent…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss…
Inside quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics.
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism.…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…