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We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson…
We quantitatively analyze the dynamics of the quantum phase distribution associated with the reduced density matrix of a system, as the system evolves under the influence of its environment with an energy-preserving quantum nondemolition…
We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange $J$ and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two…
As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…
System of Dirac fermions with random-varying mass is studied in detail. We reformulate the system by transfer-matrix formalism. Eigenvalues and wave functions are obtained numerically for various configurations of random telegraphic mass…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between…
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…
We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising…
We introduce a network model to describe two-dimensional disordered electron systems with spin-orbit scattering. The network model is defined by a discrete unitary time evolution operator. We establish by numerical transfer matrix…
Today, the competition to build a quantum computer continues, and the number of qubits in hardware is increasing rapidly. However, the quantum noise that comes with this process reduces the performance of algorithmic applications, so…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
We study the localization transition in periodically driven one-dimensional non-Hermitian lattices where the piece-wise two-step drive is constituted by uniform coherent tunneling and incommensurate onsite gain and loss. We find that the…
We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via…
We study a fermionic two-band model with the interband transition resonantly coupled to a cavity. This model was recently proposed to explain cavity-enhanced charge transport, but a thorough characterization of the closed system, in…
We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…
The destruction of quantum-mechanical phase coherence by a fluctuating quantum bath has been investigated mostly for a single particle. However, for electronic transport through disordered samples and mesoscopic interference setups, we have…
We describe a method allowing transient suppression of decoherence effects on the atom-optics realization of the kicked rotor. The system is prepared in an initial state with a momentum distribution concentrated in an interval much sharper…