Related papers: Krein systems with oscillating potentials

We consider damped $s$-fractional Klein--Gordon equations on $\mathbb{R}^d$, where $s$ denotes the order of the fractional Laplacian. In the one-dimensional case $d = 1$, Green (2020) established that the exponential decay for $s \geq 2$…

Ochiai has previously proved that the Beilinson-Kato Euler systems for modular forms interpolate in nearly-ordinary $p$-adic families (Howard has obtained a similar result for Heegner points), based on which he was able to prove a half of…

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling…

Invisible decays of neutral hadrons are evaluated as ordinary-mirror particle oscillations using the newly developed mirror matter model. Assuming equivalence of the $CP$ violation and mirror symmetry breaking scales for neutral kaon…

Hawking radiation has become experimentally testable thanks to the many analogue systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion, and give rise to a numerically…

Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…

We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference…

The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this…

In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…

Let $S(t)$ denote the argument of the Riemann zeta-function, defined as $$ S(t)=\dfrac{1}{\pi}\,\Im\log\zeta(1/2+it). $$ Assuming the Riemann hypothesis, we prove that $$ S(t)=\Omega_{\pm}\bigg(\dfrac{\log t\log\log\log t}{\log\log…

We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique…

We derive the general rules of functional integration in the theories of the Schwarzian type, and evaluate explicitly the functional integrals assigning correlation functions in the SYK model.

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a non-equilibrium quantum system with a critical point phase-transition, that is also known to exhibit…

We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…

Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment can be understood as the difference between the free energy of the total system and that of the bare…

By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass

We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform with respect to the oscillations of the damping, and in…

We generalize an orthonormality relation between decay eigenmodes of equilibrium systems to nonequilibrium markovian generators which commute with their time-reversal. Viewing such modes as tangent vectors to the manifold of statistical…

Using the integral representations of the solutions of Schr\"odinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the…