Related papers: Many-body States and Operator Algebra for Exclusio…
The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their…
Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner. However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow…
Isolated quantum systems typically follow the eigenstate thermalization hypothesis, but there are exceptions, such as many-body localized (MBL) systems and quantum many-body scars. Here, we present the study of a weak violation of MBL due…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups,…
Semi-annihilation is a generic feature of dark matter theories stabilised by symmetries larger than a $Z_2$. It contributes to thermal freeze out, but is irrelevant for direct and collider searches. This allows semi-annihilating dark matter…
The detailed study of disembodiment of physical properties by pre- and post-selection is present. A criterion is given to disembody physical properties for single particle with multiple degrees of freedom. It is shown that the non-commute…
New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for…
We present a method for approximating the many-body density of states of a system of quantum identical particles, with a reduction of the computational cost by a combinatorial factor compared to the full calculation. This is carried out by…
We identify raising and lowering operators of the de Sitter algebra with focus on their action on states in particular in 4 spacetime dimensions. There isn't a unique solution to the question of how the de Sitter ladder operators act on…
A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lam\'e operators.
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
Algebraic and analytic aspects of self-adjoint operators of order four or more with polynomial coefficients are investigated. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques.
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
We develop a scheme to prepare a desired state or subspace in high-dimensional Hilbert-spaces using repeated applications of a single static projection operator onto the desired target and fixed unitary dynamics. Benchmarks against other…
The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum…