Related papers: Approximate transitivity property and Lebesgue spe…
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those…
Quasi-periodic lattice systems offer diverse transport properties. In this work, we investigate the environment induced effects on transport properties for quasi-periodic systems, namely the one-dimensional Aubry-Andr\'e-Harper (AAH)…
In this work we illustrate the resurgent structure of the $\lambda$-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an $SU(N)_k$ Wess-Zumino-Witten conformal fixed point in the UV. To do so we use…
We derive the transport properties of a quantum dot subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz, a generalization of the traditional Thermodynamic Bethe Ansatz to open…
We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations $T:[0,1]\rightarrow [0,1]$ which exhibit both mixing and rigidity behavior along families of asymptotically…
Hesselholt defined a spectrum $\operatorname{TP}(X)$, the periodic topological cyclic homology of a scheme $X$, using topological Hochschild homology and the Tate construction, which is a topological analogue of Connes-Tsygan periodic…
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…
In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its…
Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established…
We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise…
A new oscillator model with different form of the non-minimal substitution within the framework of the Duffin-Kemmer-Petiau equation is offered. The model possesses exact solutions and a discrete spectrum of high degeneracy. The distinctive…
We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities, that…
We establish almost sure invariance principles (ASIP), a strong form of approximation by Brownian motion, for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations…
In this work we first show a simple approach to constructing non-Hermitian Hamiltonians with a real spectrum, which are \textit{not} obtained by a non-unitary transformation such as the imaginary gauge transformation. They are given,…
The possibility that a short-range interacting system exhibits nonadditivity is investigated. After the discussion on the precise definition of additivity and its consequence, we show that it is possible when the system is in a…
We study the class of transitive skew-products associated with iterated function systems of circle diffeomorphisms. We can approximate any transitive skew-product by maps in this class that have a robustly zero Lyapunov exponent. In…
We first analyse the integrable scattering theory describing the massless excitations of $AdS_2 \times S^2 \times T^6$ superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured…
A family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian entries is considered. The asymptotic spectral distribution in these models is uniform in…