Related papers: Quantum Disordered Systems with a Direction
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…
We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to…
Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex…
The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of…
The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The…
The eigenspectrum of a non-normal matrix, which does not commute with its Hermitian conjugate, is a central issue of non-Hermitian physics that has been extensively studied in the past few years. There is, however, another characteristic of…
Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the…
We investigate the quantum properties of a non-random Hamiltonian with a step-like singularity. It is shown that the eigenfunctions are multifractals and, in a certain range of parameters, the level statistics is described exactly by…
. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…
Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…
In this work, we discuss a non-Hermitian system described via a one-dimensional single-particle tight-binding model, where the non-Hermiticity is governed by random nearest-neighbour tunnellings, such that the left-to-right and…
We investigate the statistical properties of eigenvalues of pseudo-Hermitian random matrices whose eigenvalues are real or complex conjugate. It is shown that when the spectrum splits into separated sets of real and complex conjugate…
The interplay between non-Hermiticity and disorder gives rise to unique universality classes of Anderson transitions. Here, we develop a field-theoretical description of non-Hermitian disordered systems based on fermionic replica nonlinear…
We consider an ensemble of large non-Hermitian random matrices of the form $\hat{H}+i\hat{A}_s$, where $\hat{H}$ and $\hat{A}_s$ are Hermitian statistically independent random $N\times N$ matrices. We demonstrate the existence of a new…
We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…