Related papers: Fast Converging Path Integrals for Time-Dependent …
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the…
We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the…
Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and…
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
We present our program for the development of quantum informational concepts in relativistic systems in terms of the unequal-time correlation functions of quantum fields. We employ two formalisms that provide the basis for further…
We present the derivation of an alternative representation of the real-time in-in formalism under a spatially homogeneous and time independent electric field. Because the system exhibits instability associated with pair production of…
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential.…
Extracting information about a system's metastable ground state energy employing functional methods usually hinges on utilizing the late-time behavior of the Euclidean propagator, practically impeding the possibility of determining decay…
In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and…
This article provides a detailed derivation of the path integral formalism for both boson and fermion quantum open systems using coherent states. The formalism on the imaginary-time axis, Keldysh contour, and Kadanoff contour are given. The…
In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy $s$-wave correlated pair and spectator particles, while terms that include energy…
The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…
We propose a new rigorous time-slicing construction of the phase space Path Integrals for propagators both in Quantum Mechanics and Quantum Field Theory for a fairly general class of quantum observables (e.g. the Schroedinger hamiltonians…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…