Related papers: Non-Hermitian Quantum Fractals
The time evolution of initially localized wavepackets in the discrete Hatano-Nelson lattice displays a rich dynamical structure shaped by the interplay between dispersion and nonreciprocity. Our analysis reveals a characteristic evolution…
Gauge potentials with different configurations have been recently realized in the optical lattice experiments. It is remarkable that one of the simplest gauge can generate particle energy spectrum with the self-similar structure known as a…
Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external…
We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter's butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter's butterfly…
We introduce a one-dimensional (1D) extended quantum breakdown model comprising a fermionic and a spin degree of freedom per site, and featuring a spatially asymmetric breakdown-type interaction between the fermions and spins. We…
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of…
In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum mechanical path of a relativistic string and…
In recent work, the so-called quasi-Zeno dynamics of a system has been investigated in the context of the quantum first passage problem. This dynamics considers the time evolution of a system subjected to a sequence of selective projective…
The Heisenberg picture for non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order…
The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…
Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian…
The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field antiferromagnetic patterns is theoretically studied. We report on a specific tight-binding model of artificial antiferromagnetic structures incorporating both…
Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral…
We experimentally simulate in a photonic setting non-Hermitian (NH) metals characterized by the topological properties of their nodal band structures. Implementing nonunitary time evolution in reciprocal space followed by interferometric…
Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here we study how quantum information and correlations spread under a quantum…
Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…
We address the nature of the antiferromagnetic quantum phase transition that separates a semimetal from an antiferromagnet in the repulsive Hubbard model defined on the honeycomb lattice. At the critical point, the fermions acquire an…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…