Related papers: Spectral Analysis of the Quantum Random Energy Mod…
It has been observed that the asymmetric quantum Rabi model (QRM), which does not possess any obvious symmetry, exhibits energy level crossings, which are often associated with symmetries. This observation suggests that there is in fact a…
The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating…
Magnetic effects on free electron systems have been studied extensively in the context of spin-to-orbital angular momentum conversion. Using a quantum field theory framework, we derive a similar relationship in the non-relativistic limit…
We introduce a novel quantum spin-glass model, a Sherrington-Kirkpatrick model with a transverse mean-field type random magnet. We rigorously derive the exact expression of the free energy of this model at the entire parameter region. The…
The average (thermal) gyroradius of charged particles is re-examined from a quantum-mechanical point of view. The straight quantum-mechanical calculation clearly reproduces its conventionally used random-mean-square (rms) expectation value.…
We study numerically the population transfer protocol on the Quantum Random Energy Model and its relation to quantum computing, for system sizes of $n\leq 20$ quantum spins. We focus on the energy matching problem, i.e. finding multiple…
We discuss the possibility of spin glass order in the vicinity of the unexpected metallic state of the two-dimensional electron gas in zero applied magnetic field. An average ferromagnetic moment may also be present, and the spin glass…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
Motivated by the Lee--Yang approach to phase transitions, we study the partition function of the Generalized Random Energy Model (GREM) at complex inverse temperature $\beta$. We compute the limiting log-partition function and describe the…
Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The…
Electron Raman scattering (ERS) is investigated in a parabolic semiconductor quantum wire in a transverse magnetic field neglecting by phonon-assisted transitions. The ERS cross-section is calculated as a function of a frequency shift and…
We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multi-mode optical cavities. The solution of an infinite-range model yields a metallic phase…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical…
Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…
We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma…
We introduce quantum spatio-temporal dynamics (QSD) as modeled by the Nexus Paradigm (NP) of quantum gravity to resolve the problem of energy-momentum localization in a gravitational field. Currently, the gravitational field as described…
We study the $\pm J$ SK model for small $N$'s up to $N=9$. We sort the $2^{N(N-1)/2}$ possible realizations of the coupling matrix into equivalence classes according to the gauge symmetry and permutation symmetry and determine the energy…
We discuss the role of quantum coherence in the energy fluctuations of open quantum systems. To this aim, we introduce a protocol, to which we refer to as the end-point-measurement scheme, allowing to define the statistics of energy changes…