Related papers: Topological pressure and equilibrium state for cer…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
Expanding Thurston maps form a class of branched covering maps on the topological $2$-sphere $S^{2}$, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption initially…
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization…
The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and…
Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth…
We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…
We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on the Momentum Constraint of General Relativity. It relates the rate of complexity variation with…
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant…
We study invariant measures and thermodynamic formalism for a class of endomorphisms $F_T$ which are only piecewise differentiable on countably many pieces and non-conformal. The endomorphism $F_T$ has parametrized countably generated limit…
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…
We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
Based on the contact Hamiltonian Floer theory established by Will J. Merry and the second author that applies to any admissible contact Hamiltonian system $(M, \xi = \ker \alpha, h)$, where $h$ is a contact Hamiltonian function on a…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…
We study the topology of the space of probability measures invariant under the geodesic flow, defined on the unit-tangent bundle of a compact Riemannian manifold with non-positive curvature. Building on a previous work by Coud\`ene and…