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We compute the spectrum of the low-lying mesonic states with vector, scalar and pseudoscalar quantum numbers in QCD with one flavour. With three colours the fundamental and the two-index anti-symmetric representations of the gauge group…
We explore the impact of commensurate multifrequency driving protocols on the stability of topological edge modes in topological 1D systems of spinless fermions. Using Floquet theory, we show that all the topological phase transitions can…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it…
We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (Quadratic Gravity) in the spherically-symmetric sector. The formulation relies on (i) harmonic gauge to cast the…
An algebraic approach is formulated in the harmonic approximation to describe a dynamics of two-fermion systems, confined in three-dimensional axially symmetric parabolic potential, in an external magnetic field. The fermion interaction is…
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are…
We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U$(1)$-symmetry in two spatial dimensions (2D). By deriving the exact fermion replica-quantum master equation, we line…
The spinless Falicov-Kimball model is studied by the use of a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the…
The hard-scattering contributions to heavy-to-light form factors at large recoil are studied systematically in soft-collinear effective theory (SCET). Large logarithms arising from multiple energy scales are resummed by matching QCD onto…
We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We…
We consider a regularised Fermi projection of the Hamiltonian of the massless Dirac equation at Fermi energy zero. The matrix-valued symbol of the resulting operator is discontinuous in the origin. For this operator, we prove Szeg\H{o}-type…
We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…
We present an alternative form of master equation, applicable on the analysis of non-equilibrium dynamics of fermionic open quantum systems. The formalism considers a general scenario, composed by a multipartite quantum system in contact…
We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained,…
We consider the V-A Fermi interaction and apply an earlier developed method for summing up the leading asymptotics for scattering amplitudes in non-renormalizable theories. We consider the amplitude of fermion-antifermion scattering and…
Let $F$ be a non-degenerate quadratic form on an $n$-dimensional vector space $V$ over the rational numbers. One is interested in counting the number of zeros of the quadratic form whose coordinates are restricted in a smoothed box of size…
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…
The spectral properties of a variety of improved staggered operators are studied in quenched QCD. The systematic dependence of the infrared eigenvalue spectrum on i) improvement in the staggered operator, ii) improvement in the gauge field…