Related papers: Bound state eigenfunctions need to vanish faster t…
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is…
For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed…
We consider the time-dependent Navier-Stokes equations in a half-space with boundary data on the line $(x,y)=(x_0,y)$ assumed to be time-periodic (or stationary) with a fixed asymptotic velocity ${\bf u}_{\infty}=(1,0)$ at infinity. We show…
In this paper we consider a class of continuity equations that are conditioned to stay in general space-time domains, which is formulated as a continuum limit of interacting particle systems. Firstly, we study the well-posedness of the…
We extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and…
The quantum speed limit sets a fundamental restriction on the evolution time of quantum systems. We explore the relationship between quantum imaginarity and the quantum speed limit by utilizing measures such as relative entropy, trace…
The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
We consider a run-and-tumble particle whose speed and tumbling rate are space-dependent on an infinite line. Unlike most of the previous work on such models, here we make the physical assumption that at large distances, these rates saturate…
We explore the border between regular and chaotic quantum dynamics, characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. This…
We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…
We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting the impurity is injected in the fluid with some initial velocity ${\mathbf v}_0$, and we are…
Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…
Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a well-known property of the anti-de Sitter…
In this exploratory study, we investigate the bounds on the equation of state of dark matter. Modeling dark matter as a fluid component, we take into account both positive and negative fixed equations of state. Using CMB, supernovae Ia and…
The asymptotic behavior in the leading order of the continuous spectrum eigenfunctions $\Psi(\bz,\bq)$ as $|\bz|\rightarrow\infty$ for the system of three three-dimensional charged quantum particles has been obtained on the heuristic level.…
In the present paper we study two challenging problems for helium-type systems. Existence of eigenvalues at thresholds and the asymptotic behavior of the corresponding eigenfunctions. Since the usual methods for addressing these problems…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…
We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, $\rho_1$ and $\rho_2$. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the…