Related papers: An integral-free representation of the Dyson serie…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

We present methods which allow orders of magnitude increase in the number of modes in linear optics experiments by moving from spatial encoding to temporal encoding and using dispersion. This enables significant practical advantages for…

We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the…

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…

We transformed the generalized exponential power series to another functional form suitable for further analysis. By applying the Cauchy-Euler differential operator in the form of an exponential operator, the series became a sum of…

We discuss dissipative systems in Quantum Field Theory by studying the canonical quantization of the damped harmonic oscillator (dho). We show that the set of states of the system splits into unitarily inequivalent representations of the…

We derive a bosonic Hamiltonian from two dimensional QCD on the light-front. To obtain the bosonic theory we find that it is useful to apply the boson expansion method which is the standard technique in quantum many-body physics. We…

The historical Klein-Gordon transformation of complex-valued first-order in time Schroedinger equations iterates these in a naively straightforward way which changes them into complex-valued second-order in time equations that have a…

Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…

We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze…

Dyson's model in infinite dimensions is a system of Brownian particles that interact via a logarithmic potential with an inverse temperature of $ \beta = 2$. The stochastic process can be represented by the solution to an…

We consider the evolution, for a time-dependent Schr\"odinger equation, of the so called Dirac comb. We show how this evolution allows us to recover explicitly (indeed optically) the values of the quadratic generalized Gauss sums. Moreover…

Optimization time integrators are effective at solving complex multi-physics problems including deformable solids with non-linear material models, contact with friction, strain limiting, etc. For challenging problems, Newton-type optimizers…

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…

This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the…

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…

We explore the possibility of adding complex absorbing potential at the boundaries when solving the one-dimensional real-time Schr\"odinger evolution on a grid using a quantum computer with a fully quantum algorithm described on a $n$ qubit…

Linear free divisors are free divisors, in the sense of K.Saito, with linear presentation matrix (example: normal crossing divisors). Using techniques of deformation theory on representations of quivers, we exhibit families of linear free…