289 Results Found

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obt...

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent p...

An exactly solvable, one-component model originating from a unitary scenario of spontaneous particle production in curved spacetimes is proposed. The properties of such a system with a time-independent and a time-dependent Hamiltonian are discussed.

Contrary to the initial-value problem for ordinary differential equations, where the classical theory of establishing the exact unique solvability conditions exists, the situation with the initial-value problem for linear functional differential equa...

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse...

A spin-boson-like model with two interacting qubits is analysed. The model turns out to be exactly solvable since it is characterized by the exchange symmetry between the two spins. The explicit expressions of eigenstates and eigenenergies make it po...

This paper presents a two-qubit model derived from an SU(2)-symmetric 4×4 Hamiltonian. The resulting model is physically significant and, due to the SU(2) symmetry, is exactly solvable in both time-independent and time-dependent cases. Using th...

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable $N\mathrm{-}$state model is considered, characterized by a non-stationary non-Hermitian Hami...

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of $N_1$ interacting bosons of mass $m_1$ driven by a force of amplitude $f_{L,1}$ and $N_2$ interacting bosons of mass $m_2$ driven by a force of amplitude $f_{L,2}$,...

We extend the scope of the unified factorization method to the solution of conditionally and unconditionally exactly solvable models of quantum mechanics, proposed in a previous paper [R.R. Nigmatullin, A.A. Khamzin, D. Baleanu, Results in Physics 41...

This paper for the first time derives some properties of the hydrogen atom inside a box with an impenetrable wall. Scaling of the Hamiltonian operator proves to be practical for the derivation of some general properties of the eigenvalues. The radial...

This review delves into the utilization of a sextic oscillator within the $\beta$ degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the $\beta$ shap...

We deal here with an exactly solvable N-nucleon system that has been used to mimic typical features of quantum many-body systems. There is in the literature some controversy regarding the possible existence of a quantum phase transition in the model....

Exact conditions for the existence of the unique solution of a boundary value problem for linear fractional functional differential equations related to $\varsigma$-nonpositive operators are established. The exact solvability conditions are based on the...

The exact conditions sufficient for the unique solvability of the initial value problem for a system of linear fractional functional differential equations determined by isotone operators are established. In a sense, the conditions obtained are optim...

The Random Domino Automaton—a stochastic cellular automaton forest-fire model—is formulated for the Bethe lattice geometry. The equations describing the stationary state of the system are derived using combinatorial analysis. The special...

Reinterpretation of mathematics behind the exactly solvable Calogero’s A-particle quantum model is used to propose its generalization. Firstly, it is argued that the strongly singular nature of Calogero’s particle–particle interacti...

This paper investigates a high-order numerical method based on a spatial compact exponential scheme for solving the time-fractional Black–Scholes model. Firstly, the original time-fractional Black–Scholes model is converted into an equiva...

This paper focuses on reduced-order modeling for contact mechanics problems treated by Lagrange multipliers. The high nonlinearity of the dual solutions lead to poor classical data compression. A hyper-reduction approach based on a reduced integratio...

We study two credit risk models with occupation time and liquidation barriers: the structural model and the hybrid model with hazard rate. The defaults within the models are characterized in accordance with Chapter 7 (a liquidation process) and Chapt...

We consider a multi-species mixture of interacting bosons, $N_1$ bosons of mass $m_1$, $N_2$ bosons of mass $m_2$, and $N_3$ bosons of mass $m_3$, in a harmonic trap with frequency $\omega$. The corresponding intra-species interaction strengths are ${\lambda }_{11}$, ${\lambda }_{}$...

We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental...

The coherent energy transfer between two identical two-level systems is investigated. Here, the first quantum system plays the role of a charger, while the second can be seen as a quantum battery. Firstly, a direct energy transfer between the two obj...

The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under c...

In Monte Carlo particle transport, it is important to change the variance of calculations of relatively rare events with a technique known as non-analog Monte Carlo. In order to reduce the variance and the computation time, biasing techniques are in...

Interval numbers comprise potential fields of application and describe the imprecision brought on by the flexible nature of data between boundaries. The recently added type-2 interval number allows a more thorough understanding of interval numbers. D...

In this paper, the behavior of a heavy hole gas in a strongly prolate ellipsoidal Ge/Si quantum dot has been investigated. Due to the specific geometry of the quantum dot, the interaction between holes is considered one-dimensional. Based on the adia...

The fact that the Ising model in higher dimensions than 1D features a phase transition at the critical temperature $T_c$ despite its apparent simplicity is one of the main reasons why it has lost none of its fascination and remains a central benchmark i...

We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the waiting t...

The many-body dynamics of an electron spin−1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath,...

Lee’s field-theoretical model describes the interaction between a qubit and a structured bosonic field. We study the mathematical properties of the Hamiltonian of the single-excitation sector of the theory, including a possibly “singular” qubit-field...

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent...

An exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting...

We introduce and prove the “root theorem”, which establishes a condition for families of operators to annihilate all root states associated with zero modes of a given positive semi-definite k-body Hamiltonian chosen from a large class. Th...

In this paper, we establish the asynchronous computability theorem in d-solo system by borrowing concepts from combinatorial topology, in which we state a necessary and sufficient conditions for a task to be wait-free computable in that system. Intui...

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number $\pi$ . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of $\pi$ in a base de...

We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assum...

Motivated by a simple model of earthquake statistics, a finite random discrete dynamical system is defined in order to obtain Catalan number recurrence by describing the stationary state of the system in the limit of its infinite size. Equations desc...

In a series of papers [1,2,3], Lawrence Schulman presented examples which demonstrate the compatibility of opposite arrows of time in various situations. In a previous letter to this journal [4] I questioned some of them for not being realistic in sp...

I argue that opposite arrows of time, while being logically possible, cannot realistically be assumed to exist during one and the same epoch of our universe.

Using the entropic quantifier called statistical complexity, we investigate the interplay between (1) pairing interactions between fermions, can be viewed as analogous with superconductivity based on Cooper pairs; (2) rotations of the system as a who...

Let us consider a two-sided multi-species stochastic particle model with finitely many particles on $\mathbb{Z}$, defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1....

We study one-dimensional stochastic particle systems with exclusion interaction—each site can be occupied by at most one particle—and homogeneous jumping rates. Earlier work of Alimohammadi and Ahmadi classified 28 Yang–Baxter integ...

Odd-even statistical staggering in a Lipkin-like few fermions model has been recently encountered. Of course, staggering in nuclear binding energies is a well established fact. Similar effects are detected in other finite fermion systems as well, as...

For a given operator $D\left(t\right)$ of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant $t_{critical}$ of a sp...

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large...

A boundary value problem is formulated for a stationary model of mass transfer, which generalizes the Boussinesq approximation in the case when the coefficients in the model equations can depend on the concentration of a substance or on spatial varia...

This work scrutinizes, using statistical mechanics indicators, important traits displayed by quantum many-body systems. Our statistical mechanics quantifiers are employed, in the context of Gibbs’ canonical ensemble at temperature T. A new quan...

A fuzzified matrix space consists of a collection of matrices with a fuzzy structure, modeling the cases of uncertainty on the part of values of different matrices, including the uncertainty of the very existence of matrices with the given values. Th...

It is well known that, using the conventional non-Hermitian but $\mathcal{PT}-$symmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable...