Related papers: Localized topological pressure and equilibrium sta…
Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
We examine uniqueness of equilibrium states for the natural extension of a topologically exact, non-uniformly expanding, local homeomorphism with a H\"older continuous potential function. We do this by applying general techniques developed…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…
Let $S$ be a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. We examine the geodesic flow on $S$ and prove local product structure for a…
We study the geodesic flow on the unit tangent bundle of a rank one manifold and we give conditions under which all classical definitions of pressure of a H\"older continuous potential coincide. We provide a large deviation statement, which…
In a quasi-one-dimensional system the particles remain ordered from left to right allowing the association of a volume element to the particle which on average resides there. Thus the properties of that single particle can give the local…
In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions. Under antisymmetry this property, also known as…
$M$ is a Riemannian, boundaryless, and compact manifold with $\dim M\geq 2$, and $f$ is a $C^{1+\beta}$ ($\beta>0$) diffeomorphism of $M$. $\varphi$ is a H\"older continuous potential on $M$. We construct an invariant and absolutely…
We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the…
We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…
A translation-invariant gapped local Hamiltonian is in the trivial phase if it can be connected to a completely decoupled Hamiltonian with a smooth path of translation-invariant gapped local Hamiltonians. For the ground state of such a…
In this paper, we show that the low energy spaces in the prescribed singularity case $\mathcal{E}_{\psi}(X,\theta,\phi)$ have a natural topology which is completely metrizable. This topology is stronger than convergence in capacity.
It is known that if $f: \mathbb{S}^{1} \rightarrow \mathbb{S}^{1}$ is a transitive $C^{1+\alpha}$-local diffeomorphism non-invertible and non-uniformly expanding, then there is a unique parameter $t_{0} \in (0 , 1]$ such that the…
Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…
In this paper we propose a self--consistent approach to the description of temporal dynamics of localized states. This approach is based on exactly solvable quantum mechanical models with multi-well potentials and their propagators. States…
A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…
Assume that $(X,f)$ is a dynamical system and $\phi:X \to [-\infty, \infty)$ is a potential such that the $f$-invariant measure $\mu_\phi$ equivalent to $\phi$-conformal measure is infinite, but that there is an inducing scheme $F = f^\tau$…
The introduction of structural defects in otherwise periodic media is well known to grant exceptional space control and localization of waves in various physical fields, including elasticity. Despite the variety of designs proposed so far,…