数学物理
In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of the many-body Schr\"odinger dynamics and prove emergence of…
We prove that the discrete Dirac operators in three dimensions converge to the continuum Dirac operators in the strong resolvent sense, but not in the norm resolvent sense.
The integrated Sachs-Wolfe (ISW) effect is a property of the Cosmic Microwave Background (CMB), in which photons from the CMB are gravitationally redshifted, causing the anisotropies in the CMB. An intriguing question is whether one can…
We study the ground state of a system of $N$ two-dimensional trapped almost-bosonic anyons subject to an external magnetic field. This setup can equivalently be viewed as bosons interacting through long-range magnetic potentials generated…
We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming…
A novel result in $\mathbb Z_2$-equivariant homotopy theory is stated, proven, and applied to the topological classification of classically frustrated magnets in the presence of canonical time-reversal symmetry. This result generalizes a…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
We present a micro-structurally based finite element model of the human cornea, where we explicitly describe the collagen-crosslink architecture in terms of a trusswork of non-linear struts, and the extracellular proteoglycan matrix in…
The slightly subtle notion of covariant Lie derivatives of \textit{bundle-valued} differential forms is crucial in many applications in physics, notably in the computation of conserved currents in gauge theories, and yet the literature on…
In this paper we consider the {\it Density Functional Theory} (DFT) framework, where a functional of the form $$F_\eps(\rho)=\eps T(\rho)+bC(\rho)-U(\rho)$$ has to be minimized in the class of non-negative measures $\rho$ which have a…
We revisit the J-matrix method for the one dimensional radial harmonic oscillator (RHO) and construct its tridiagonal matrix representation within an orthonormal basis phi(z)n of L2 (R+);parametrized by a fixed z in the complex unit disc D…
We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously relaxing the invertibility condition as seen in standard…
The description of the $\mathbb{Z}_2\times\mathbb{Z}_2$-graded special linear Lie superalgebra $\mathfrak{sl} (m_1+1,m_2|n_1,n_2)$ is carried out via generators $a_1^\pm,\ldots, a_{m_1+m_2+n_1+n_2}^\pm$ that satisfy triple relations and are…
The \emph{max-flow min-cut theorem} has been recently used in the theory of random tensor networks in quantum information theory, where it is helpful for computing the behavior of important physical quantities, such as the entanglement…
We present a closed-form, exact analytical solution, valid at finite times, to a class of multiple integrals with highly oscillatory kernels. Our approach leverages the intimate connection between these integrals and the minimal…
We construct families of rotationally symmetric toroidal domains in $\mathbb R^3$ for which the eigenfields associated to the first (positive) Amp\`erian curl eigenvalue are symmetric, and others for which no first eigenfield is symmetric.…
This paper focuses on the conditions for obtaining auxetic, i.e. with a negative Poisson's ratio, composite laminates made of specially orthotropic layers. In particular, the layers considered are of three types: R1-orthotropic, i.e.…
For random matrix ensembles with unitary symmetry, there is interest in the large $N$ form of the moments of the absolute value of the characteristic polynomial for their relevance to the Riemann zeta function on the critical line, and to…
This paper investigates the initial boundary value problem of a finitely degenerate semilinear pseudo-parabolic equation associated with H\"{o}rmander's operator. Based on the global existence of solutions in previous literature, the…