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Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential
In this chapter, wePeriodic potential give complete spectral analysis of the Schrödinger operatorSchrödinger operator L(q) with an arbitrary locally...
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Entanglement of harmonic systems in squeezed states
The entanglement entropy of a free scalar field in its ground state is dominated by an area law term. It is noteworthy, however, that the study of...
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On the Special Potentials
In this chapter, we study the one-dimensional Schrödinger operator L(q) with even, PT-symmetric and some other special potentials. In Sect. 3.1, we...
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Entanglement entropies of an interval in the free Schrödinger field theory at finite density
We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrödinger field theory at finite density and...
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Late time behavior of n-point spectral form factors in Airy and JT gravities
We study the late time behavior of n -point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, which includes both...
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The Heat Kernel on the Diagonal for a Compact Metric Graph
We analyze the heat kernel associated with the Laplacian on a compact metric graph, with standard Kirchhoff–Neumann vertex conditions. An explicit...
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On the Global Minimum of the Energy–Momentum Relation for the Polaron
For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at...
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On the stability and deformability of top stars
Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically...
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Breathers in the Fractional Frenkel-Kontorova Model
In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically...
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Strong Cosmic Censorship in Kerr-Newman-de Sitter
Christodoulou’s formulation of Strong Cosmic Censorship (SCC) holds true for Kerr-de Sitter black holes. On the other hand, Reissner-Nordström-de...
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Abnormal Transmission of Elastic Waves through a Thin Ligament Connecting Two Planar Isotropic Waveguides
AbstractThe asymptotics of the transmission and reflection coefficients for a longitudinal wave incoming from infinity and scattering in a resonator,...
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Discrete analogue of the Weil-Petersson volume in double scaled SYK
We show that the connected correlators of partition functions in double scaled SYK model can be decomposed into “trumpet” and the discrete analogue...
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Testing General Relativity with Black Hole Quasi-normal Modes
The purpose of this chapter is to provide an overview of the exciting field of black hole quasi-normal modes and its capabilities to test general...
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Asymptotic Performance of Port-Based Teleportation
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient,...
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The Discrete Spectrum and the Continuum
One-body Hamiltonians play an important role in the study of many-body quantum systems. Indeed, the multiple inter-nucleon correlations between the A...
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Modal and Non-Modal Stability of the Heated Flat-Plate Boundary Layer with Temperature-Dependent Viscosity
AbstractThis paper presents a modal and non-modal stability analysis of the boundary layer developed on a hot plate. A liquid-type...
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End of the world brane in double scaled SYK
We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model. We find that the boundary state of EOW brane is a coherent state of the q ...
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Supersymmetric phases of AdS4/CFT3
We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS 4 ...