Related papers: Quantum chaos in one dimension?
Let $\phi(x) = |1 - \frac 1x|$ for all $x > 0$. Then we extend $\phi(x)$ in the usual way to become a continuous map from the compact topological (but not metric) space $[0, \infty]$ onto itself which also maps the set of irrational points…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
In a prior paper, the author described an instability in a nonlinear wavefunction model. Proposed in connection with the Measurement Problem, the model contained an external potential creating a ``classical'' instability. However, it is…
{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor…
Motivated by some recent speculative attempts to model the dark energy, scalar fields with negative kinetic energy coupled to gravity without a cosmological constant are considered. It is shown that in the presence of an ordinary fluid, any…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as…
We consider the BVP $-y" + qy = \lambda y$ with $y(0)=y(1)=0$. The inverse spectral problems asks one to recover $q$ from spectral information. In this paper, we present a very simple method to recover a potential by sampling one…
Non-separable $D-$dimensional partial differential Schr\"{o}dinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case)…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an…
The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering…
Chaos synchronization in one of charge-carrier dynamical systems in photoconductors is studied within both the replica and nonreplica approaches.It has been shown that using the boundedness of the solutions of the dynamical systems,…
The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
We study the quantum mechanics of a system with inverse square potential in noncommutative space. Both the coordinates and momentums are considered to be noncommutative, which breaks the original so(2,1) symmetry. The energy levels and…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
We study non-Gaussian log-correlated multiplicative chaos, where the random field is defined as a sum of independent fields that satisfy suitable moment and regularity conditions. The convergence, existence of moments and analyticity with…