Related papers: Path Integral Solution of a Class of Explicitly Ti…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
The path-integral of the fermionic oscillator with a time-dependent frequency is analyzed. We give the exact relation between the boundary condition to define the domain in which the path-integral is performed and the transition amplitude…
Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for…
This paper introduces a new transformer-based model for the problem of travel time estimation. The key feature of the proposed GCT-TTE architecture is the utilization of different data modalities capturing different properties of an input…
A space-time symmetric and explicitly Lorentz covariant path integral formalism of relativistic quantum mechanics is proposed, which produces partial locally correlations of quantum processes of massive particles with the velocity of light…
Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density…
We show how the induction law is correctly used in the path integral computation of the free particle propagator. The way this primary path integral example is treated in most textbooks is a little bit missleading.
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…
Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the…
We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…
Path integral solutions with kinetic coupling potentials $\propto p_1p_2$ are evaluated. As examples I give a Morse oscillator, i.e., a model in molecular physics, and the double pendulum in the harmonic approximation. The former is solved…
We develop the formulation of the spin(SU(2)) coherent state path integrals based on arbitrary fiducial vectors. The resultant action in the path integral expression extensively depends on the vector; It differs from the conventional one in…
We explore properties of path integral complexity in field theories on time dependent backgrounds using its dual description in terms of Hartle-Hawking wavefunctions. In particular, we consider boundary theories with time dependent…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
We consider the inverse problem of determining a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $\Omega$ a $C^2$ bounded domain of $\mathbb R^n$, $n\geq2$, from…
We present a direct path integral derivation of the propagator in the presence of a step potential. The derivation makes use of the Path Decomposition Expansion (PDX), and also of the definition of the propagator as a limit of lattice…
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…