Related papers: Quantitative uncertainty principles for time-frequ…
We extend previous halo effective field theory analyses of low-energy elastic scattering of $^{3}$He-$^{4}$He, including the $\frac{7}{2}^{-}$ $f$-wave resonance as an explicit degree of freedom. The presence of this resonance necessitates…
Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states…
We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities,…
A vast literature over the past fifteen years has been devoted to the study of the geometric properties of Gaussian random waves. In this work, we investigate the geometric behavior of \emph{uniform random waves}, a much less studied…
Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded…
Let $sym^{2} f$ denote the symmetric square lift of a Hecke eigenform $f \in S_{k}(\Gamma_{0}(N))$ with the $n^{\rm th}$-Fourier coefficients $ \lambda_{sym^{2}f}(n)$. In this article, we prove an estimate for the first moment of the…
Quantum effects arising from manifestly broken time-reversal symmetry are investigated using time-dependent perturbation theory in a simple model. The forward time and the backward time Hamiltonians are taken to be different and hence the…
Consider a finite dimensional complex Hilbert space $\cH$, with $dim(\cH) \geq 3$, define $\bS(\cH):= \{x\in \cH \:|\: ||x||=1\}$, and let $\nu_\cH$ be the unique regular Borel positive measure invariant under the action of the unitary…
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic…
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we…
Propagation of a localised wave function of a massive scalar field is investigated in its rest frame. The complete orthogonal Hermite-Gauss basis is presented, and the Gouy phase and Rayleigh scale notions are adapted. The leading and…
Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution…
In this article, we study the time-reversal properties of a generic Markovian stochastic field dynamics with Gaussian noise. We introduce a convenient functional geometric formalism that allows us to straightforwardly generalize known…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
We prove a new version of the Uncertainty Principle of the form $\int |f|^2 \lesssim \int_{E^c} |f|^2 + \int_{\Sigma ^c}|\hat f|^2 $ where the sets $E$ and $\Sigma$ are $\epsilon$-thin in the following sense: $|E \cap D(x, \rho_1(x))| \le…
We consider large random matrices $X$ with centered, independent entries but possibly different variances. We compute the normalized trace of $f(X) g(X^*)$ for $f,g$ functions analytic on the spectrum of $X$. We use these results to compute…