Related papers: Quantum Hopfield Model
Typically in many-body systems the correlation energy, which is defined as the difference between the exact ground state energy and the mean-field solution, has been a measure of the system's total correlations. However, under the quantum…
The Helmholtz free energy of oscillators in thermal equilibrium with electromagnetic radiation is obtained from the Pauli-Hellmann-Feynman theorem and applied to some aspects of Lamb shifts and van der Waals interactions.
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
We introduce a Hamiltonian coupling Majorana fermion degrees of freedom to a quantum dimer model. We argue that, in three dimensions, this model has deconfined quasiparticles supporting Majorana zero modes obeying nontrivial statistics. We…
We present extensive simulations of a quantum version of the Hopfield Neural Network to explore its emergent behavior. The system is a network of $N$ qubits oscillating at a given $\Omega$ frequency and which are coupled via Lindblad jump…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
The collective Hamiltonian including isovector pairing and $\alpha$-particle type correlation degrees of freedom is constructed. The Hamiltonian is applied to description of the relative energies of the ground states of even-even nuclei…
In this paper we investigate a family of models for a qubit interacting with a bosonic field. More precisely, we find asymptotic limits of the Hamiltonian as the strength of the interaction tends to infinity. The main result has two…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement…
Understanding how strong coupling and memory effects influence the energy levels of open quantum systems is a complex and challenging problem. Here, we show these effects by probing the transition frequency of an open two-level system…
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature,…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
System of the quantum Langevin equations for two quantum coupling oscillators within independent heat baths of quantum oscillators are obtained using a model Hamiltonian and corresponding Heisenberg equations of motion. Expressions for mean…
We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $\delta$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…