相关论文: $\widetilde{O}(N^2)$ Representation of General Con…

A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…

We deal with the following system of coupled asymmetric oscillators \[ \begin{cases} \ddot{x}_1+a_1x_1^+-b_1x^-_1+\phi_1(x_2)=p_1(t) \\ \ddot{x}_2+a_2\,x_2^+-b_2\,x^-_2+\phi_2(x_1)=p_2(t) \end{cases} \] where $\phi_i: \mathbb{R} \to…

We are motivated by tripartite entanglement for fermions. While GHZ or W states involve 3-fold intrication, we consider here piecewise intrication of 3 fermions in ${\bf C}^2$, namely of type $ab+bc+ca$. Before interaction with…

Following Ref. [Oriols X 2007 Phys. Rev. Lett., 98 066803], an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it…

Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational…

We propose group theory interpretation of the integral representation of the quantum open Toda chain wave function due to Givental. In particular we construct the representation of $U((\mathfrak{gl}(N))$ in terms of first order differential…

We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral…

This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…

Consider a system of $N$ electrons projected onto the lowest Landau level (LLL) with filling factor of the form $n/(2pn\pm1)<1/2$ and $N$ a multiple of $n$. We show that there always exists a two-dimensional symmetric correlation factor…

We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our…

We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the…

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with $SO(1,1)\times SO(2)$ symmetry, which is the feature arising when one has only space-space noncommutativity ($\theta_{0i}=0$), we prove that the…

The basic question is addressed, how the space dimension $d$ is encoded in the Hilbert space of $N$ identical fermions. There appears a finite number $N!^{d-1}$ of many-body wave functions, called shapes, which cannot be generated by…

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface of metallic materials. The method introduces a set of numerically calculated generalized…

We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space…

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density…

The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body…

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the…