Related papers: Fractional Quantum Mechanics and Levy Path Integra…
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional L\'evy processes are defined by integrating…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
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.
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
We discuss dual time evolution scenarios which, albeit running according to the same real time clock, in each considered case may be mapped among each other by means of an analytic continuation in time. This dynamical duality is a generic…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the…
We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…