Related papers: Quantum revivals and carpets in some exactly solva…
We investigate the behavior of the Schr\"odinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational…
We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the…
We study the dynamics and predictions of a new emergent-universe model recently derived within Quantum Reduced Loop Gravity and based on the so-called statistical regularization scheme. These effective geometries show a dynamical transition…
By putting two harmonic oscillator potential $x^2$ side by side with a separation $2d$, two exactly solvable piecewise analytic quantum systems with a free parameter $d>0$ are obtained. Due to the mirror symmetry, their eigenvalues $E$ for…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
We show that a charged fluid endowed with an internal spin degree of freedom naturally satisfies the Pauli equation for a nonrelativistic spin-1/2 particle, and that a collection of n such interacting fluids can be reformulated as an Euler…
A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained…
The edge of the electronic fractional quantum Hall (FQH) system obeys the law of the chiral Luttinger liquid theory due to its intrinsic topological properties and the relation of bulk-edge correspondence. However, in a realistic…
Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of…
Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
The dynamics of a single quantum state embedded in one or several (quasi-)continua is one of the most studied phenomena in quantum mechanics. In this work we investigate its discrete analogue and consider short and long time dynamics based…
Transport experiments provide conflicting evidence on the possible existence of fractional order within integer quantum Hall systems. In fact integer edge states sometimes behave as monolithic objects with no inner structure, while other…
We present quasi-analytical and numerical calculations of Gaussian wave packet solutions of the Schr\"odinger equation for two-dimensional infinite well and quantum billiard problems with equilateral triangle, square, and circular…
We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits…
Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…