Related papers: From path integrals to dynamical algebras: a macro…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
In the present manuscript, we employ the Feynman path integral method to derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. To verify our findings we calculate the propagator associated with the free particle and the…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
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…
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
The path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet…
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
Reliable processing of quantum information is a milestone to achieve for the deployment of quantum technologies. Uncontrolled, out-of-equilibrium sources of decoherence need to be characterized in detail for designing the control of quantum…
We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…