Related papers: Computing local properties in the trivial phase

We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…

We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with…

Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant…

An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…

We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…

A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…

Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker -- the Chern number expressed in terms…

Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…

All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…

We discuss the topology of the parameter space of invertible phases with an onsite symmetry $G$, i.e., quantum many-body ground states that have neither fractionalization nor spontaneous breaking of the symmetry. The classification of…

It is shown how in principle for non-abelian gauge theories it is possible in the finite volume hamiltonian framework to make sense of calculating the expectation value of ||A||^2=\int d^3x(A^a_i(x))^2. Gauge invariance requires one to…

A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…

We give the first polynomial time algorithm for \emph{list-decodable covariance estimation}. For any $\alpha > 0$, our algorithm takes input a sample $Y \subseteq \mathbb{R}^d$ of size $n\geq d^{\mathsf{poly}(1/\alpha)}$ obtained by…

In this paper, we give a complete real-variable theory of local variable Hardy spaces. First, we present various real-variable characterizations in terms of several local maximal functions. Next, the new atomic and the finite atomic…

It is shown that if a real value PL-invariant of closed combinatorial manifolds admits a local formula that depends only on the f-vector of the link of each vertex, then the invariant must be a constant times the Euler characteristic.

The Cheeger inequalities give an upper and lower bound on the spectral gap of discrete Laplacians defined on a graph in terms of the geometric characteristics of the graph. We generalise this approach and we employ it to determine if a…

For the one-dimensional Helmholtz equation we write the corresponding time-dependent Helmholtz Hamiltonian in order to study it as an Ermakov problem and derive geometrical angles and phases in this context

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…