Browsing Mathematics by Subject "math-ph"
Now showing items 1-13 of 13
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Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model
(AIP Publishing, 2022-08-12)We provide a systematic treatment of boundaries based on subgroups K ⊆ G for the Kitaev quantum double D(G) model in the bulk. The boundary sites are representations of a -subalgebra Ξ ⊆ D(G) and we explicate its structure ... -
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
(2021)In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness ... -
Counting equilibria of large complex systems by instability index
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction ... -
Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $\mathbb R^n$, ... -
Direct and Inverse problems for time-fractional pseudo-parabolic equations
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving ... -
EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity
(2017-12)We present a new public package "EFTofPNG" for high precision computation in the effective field theory of post-Newtonian (PN) Gravity, including spins. We created this package in view of the timely need to publicly share ... -
Exact solution of pulled, directed vesicles with sticky walls in two dimensions
We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution we derive the phase diagram for this model and elucidate ... -
Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition
We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions ... -
Hardy inequalities on metric measure spaces, II: The case $p>q$
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on ... -
On Agmon metrics and exponential localization for quantum graphs
(Springer Verlag, 2018-03-28)We investigate the rate of decrease at infinity of eigenfunctions of quantum graphs by using Agmon's method to prove $L^2$ and $L^\infty$ bounds on the product of an eigenfunction with the exponential of a certain metric. ... -
Quantum geodesics in quantum mechanics
(2019-12-23) -
Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the ... -
The topological Dirac equation of networks and simplicial complexes
(IOP Publishing, 2021-09-14)We define the topological Dirac equation describing the evolution of a topological wave function on networks or on simplicial complexes. On networks, the topological wave function describes the dynamics of topological ...