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We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalise the Gaussian part of the action and calculate the propagator. Unlike…
Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
Two single-particle sources coupled in series to a chiral electronic waveguide can serve as a probabilistic source of two-particle excitations with tunable properties. The second-order correlation function, characterizing the state of…
We study the effect of a quantum Frobenius twist on Ext-groups in the category of quantum polynomial functors. We use quantum versions of the de Rham and Koszul complexes, and compute their homologies. We use them to do several…
The concept of quasi-bosons or composite bosons (like mesons, excitons etc.) has a wide range of potential physical applications. Even composed of two pure fermions, the quasi-boson creation and annihilation operators satisfy non-standard…
In frustrated antiferromagnets with isotropic exchange interactions, there is typically a manifold of degenerate classical ground states. This degeneracy is broken by the (free) energy of quantum or thermal fluctuations, or the uniform…
In this work electronic structures and optical properties of organic-inorganic exciton and polaritons in two-dimensional heterostructures combining both organic and semiconductor materials are studied. In those systems, Wannier-Frenkel…
We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean setup to study fundamental properties of excitons, ranging from condensation…
Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
A derivation of pilot waves from electrodynamic self-interactions is presented. For this purpose, we abandon the current paradigm that describes electrodynamic bodies as point masses. Beginning with the Li\'enard-Wiechert potentials, and…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
We find a unitary operator which asymptotically diagonalizes the Tomonaga-Luttinger hamiltonian of one-dimensional spinless electrons. The operator performs a Bogoliubov rotation in the space of electron-hole pairs. If bare interaction of…
The study of the fundamental properties of phonons is crucial to understand their role in applica- tions in quantum information science, where the active use of phonons is currently highly debated. A genuine quantum phenomenon associated…
Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet…
A fractional quantum Hall liquid with multiple edges is considered. The computation of transport quantities such as current, noise and noise cross correlations in such multiple edge samples requires the implementation of so called Klein…