Related papers: Grassmann Phase Space Methods for Fermions. II. Fi…
We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall…
Although the internal spaces describing spins and charges of fermions' and bosons' second-quantised fields have such different properties, yet we can all describe them equivalently with the ``basis vectors'' which are a superposition of odd…
We give a detailed discussion of the recently developed Generalized Dynamical Mean-Field Theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is non-perturbative and exact in infinite dimensions and…
We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is…
Notions of a Gaussian state and a Gaussian linear map are generalized to the case of anticommuting (Grassmann) variables. Conditions under which a Gaussian map is trace preserving and (or) completely positive are formulated. For any…
Unambiguous isospin violation in the strong interaction sector is a key issue in low energy hadronic physics, both experimentally and theoretically. Bernstein has employed the Fermi-Watson theorem to demonstrate that pion photoproduction is…
We construct a density functional theory for two-dimension electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the…
In this work, the use of the Boltzmann collision operator for dissipative quantum transport is analyzed. Its mathematical role on the description of the time-evolution of the density matrix during a collision can be understood as processes…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
The Wigner-Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean…
Duality transformations play a very important role in theoretical physics. In this paper I propose new duality transformations for fermionic theories. They map the strong coupling regime of one theory to the weak coupling regime of another…
We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original…
We numerically study a gas of two-component fermions coupled to a transversely pumped optical cavity and confined to a two-dimensional static square optical lattice. In the dispersive regime, the steady state of the system is described by…
The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations,…
The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators $\gamma^a$, offers in $d=2(2n+1)$-dimensions, such as $d=(13+1)$, a unified…
The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the…
Curvature induced phase transition is thoroughly investigated in a four- fermion theory with $N$ components of fermions for arbitrary space-time dimensions $(2 \leq D < 4)$. We adopt the $1/N$ expansion method and calculate the effective…
Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and…
We study the density-wave states of quasi-one-dimensional atomic gas mixture of one- and two-component boson and fermion using the mean-field approximation. Owing to the Peierls instability in the quasi-one-dimensional fermion system, the…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…