Related papers: On first-order scaling intertwining in quantum mec…
We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q>4, separating the…
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
One of the most important issues of quantum engineering is the construction of low-dimensional structures possessing desirable properties. For example, in different areas of possible applications of the structures containing quantum wells…
We investigate how unitary control can improve parameter estimation by designing the effective spectrum of the imprinting Hamiltonian. We show that, for commuting Hamiltonians, the general problem of spectral manipulation via unitary…
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
Tunneling between a point contact and a one-dimensional wire is usually described with the help of a tunneling Hamiltonian that contains a delta function in position space. Whereas the leading order contribution to the tunneling current is…
We present a microscopic quantum theory of intersubband polarons, quasiparticles originated from the coupling between intersubband transitions and longitudinal optical phonons. To this aim we develop a second quantized theory taking into…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
Pascal's triangle is widely used as a pedagogical tool to explain the "first-order" multiplet patterns that arise in the spectra of $I_N S$ coupled spin-1/2 systems in magnetic resonance. Various other combinatorial structures, which may be…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
The investigation of the first-order quantum phase transition (QPT) is far from clarity in comparison to that of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
It was recently shown that tunneling wavefunction proposal is consistent with loop quantum geometry corrections including both holonomy and inverse scale factor corrections in the gravitational part of a spatially closed isotropic model…
Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The…
The quantum repeater protocol is a promising approach to implement long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve efficient…