Related papers: Group word dynamics from local random matrix Hamil…
We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our…
Using simple algebraic methods along with an analogy to the BFSS model, we explore the possible (target) spacetime symmetries that may appear in a matrix description of de Sitter gravity. Such symmetry groups could arise in two ways, one…
We obtain the quantum phase diagram of the ionic Hubbard model including electron-hole symmetric density-dependent hopping. The boundaries of the phases are determined by crossing of excited levels with particular discrete symmetries, which…
For one-dimensional random Schr\"odinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Pr\"ufer phase dynamics. This paper develops a controlled perturbation theory for…
We have developed an ensemble density functional theory which includes spin degrees of freedom for nonuniform quantum Hall systems. We have applied this theory using a local-spin-density approximation to study the edge reconstruction of…
We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random…
We introduce a notion of covolume for point sets in locally compact groups that simultaneously generalizes the covolume of a lattice and the reciprocal of the Beurling density for amenable, unimodular groups. This notion of covolume arises…
Abbreviated Abstract: We study correlated states in a circular and linear-chain configuration of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective…
Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic)…
Classically the kinetic theory for a perfect gas has zero spatial number density correlation between separate points because the particles are independent. But the joint spatial and temporal correlation is non-zero (and easily calculable)…
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…
We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small…
We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a…
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector…
We consider a random Hamiltonian $H:\Sigma\to\mathbb R$ defined on a compact space $\Sigma$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy…
We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant…