Related papers: The Quantum Spherical Spin Glass Model: A Limitati…
The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, $OSP(2|1)$, as such a symmetry. A number of exactly…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between…
By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin glass order. In particular, we observe that quantum and classical spin glasses exhibit…
The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the…
Spin-orbital entanglement in the ground state of a one-dimensional SU(2)$\otimes$SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For $S=1/2$ spins and $T=1/2$ pseudospins one finds that the quantum…
The strongest evidence for superiority of quantum annealing on spin glass problems has come from comparing simulated quantum annealing using quantum Monte Carlo (QMC) methods to simulated classical annealing [G. Santoro et al., Science 295,…
This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO…
This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for…
We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic…
We consider the problem of a central spin with arbitrary spin s that interacts pairwise and uniformly with a bath of N spins with s=1/2. We present two approaches for determining the exact spectrum of this model, one based on properties of…
We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the…
We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random…
The ability of the Quantum Approximate Optimization Algorithm (QAOA) to deliver a quantum advantage on combinatorial optimization problems is still unclear. Recently, a scaling advantage over a classical solver was postulated to exist for…
I distinguish two types of reduction within the context of quantum-classical relations, which I designate "formal" and "empirical". Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two…