Related papers: Hermite expansions and Hardy's theorem
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions.…
We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the…
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also…
Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to…
We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of…
We prove that any stable method for resolving the Gibbs phenomenon - that is, recovering high-order accuracy from the first $m$ Fourier coefficients of an analytic and nonperiodic function - can converge at best root-exponentially fast in…
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…
We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation…
We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support…
An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The…
This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the…
It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero…
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.…
Single-component quantum gas confined in a harmonic potential, but otherwise isolated, is considered. From the invariance of the system of the gas under a displacement-type transformation, it is shown that the center of mass oscillates…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
In this paper we study the large time asymptotic behaviour of the heat equation with Hardy inverse-square potential on corner spaces $\mathbb{R}^{N-k}\times (0,\infty)^k$, $k\geq 0$. We first show a new improved Hardy-Poincar\'{e}…
A nonperturbative theory of multiphonon anharmonic decay of strongly excited local mode is developed whereby the mode is considered classically and phonons, quantum mechanically. The decay rate of the mode is expressed via the negative…
We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables $x$ and $p$, then so do all of its derivatives, i.e., it is a Schwartz function on phase…
We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence…