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In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wavefunction for the $\nu$ = 5/2 fractional quantum Hall state…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
Recent experimental progress in the creation of synthetic electric and magnetic fields, acting on cold atoms in a two-dimensional lattice, has attracted renewed interest to the problem of a quantum particle in the Hall configuration. The…
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…
Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…
Hilbert Spaces of bounded one dimensional non-linear oscillators are studied. It is shown that the eigenvalue structure of all such oscillators have the same general form. They are dependent only on the ground state energy of the system and…
Quantum metrology allows for a huge boost in the precision of parameters estimation. However, it seems to be extremely sensitive on the noise. Bound entangled states are states with large amount of noise what makes them unusable for almost…
It is often remarked in the literature that particles in QFT on curved spacetime are akin to coordinates in general relativity and hence are physically meaningless. This moral is given an explicit demonstration by giving the correspondence…
We consider entanglement in a system of fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
Certain unitary-invariants, known as Bargmann invariants or multivariate traces of quantum states, have recently gained attention due to their applications in quantum information theory. However, determining the boundaries of sets of…
We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating…
We study the extent to which \psi-epistemic models for quantum measurement statistics---models where the quantum state does not have a real, ontic status---can explain the indistinguishability of nonorthogonal quantum states. This is done…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…