Related papers: Commuting Quantum Matrix Models
With Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem…
We define a random commuting $d$-tuple of $n$-by-$n$ matrices to be a random variable that takes values in the set of commuting $d$-tuples and has a distribution that is a rapidly decaying continuous weight on this algebraic set. In the…
We study the ground state ordering of quadrupolar ordered $S=1$ magnets as a function of spin dilution probability $p$ on the triangular lattice. In sharp contrast to the ordering of $S=1/2$ dipolar N\'eel magnets on percolating clusters,…
In a locally interacting many-body system, two isolated qubits, separated by a large distance $r$, become correlated and entangled with each other at a time $t \ge r/v$. This finite speed $v$ of quantum information scrambling limits quantum…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
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…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation.…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
This paper explores the potential contribution of quantum computing, specifically the Variational Quantum Eigensolver (VQE), into atmospheric physics research and application problems using as an example the Lorenz system, a paradigm of…
We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal…
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular…
In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on a $N$-dimensional sphere, with $N\to \infty$, and subjected to a set of randomly placed hard-wall potentials. This model has several…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…