From AdS to Schrödinger/Lifshitz dual space-times without or with hyperscaling violation

Thermodynamics of Schrödinger black holes with hyperscaling violation

In this work, we follow Kim and Yamada (JHEP1107 (2011) 120) and utilize AdS in light-cone frame to derive thermodynamic and transport properties of two kinds of Schrödinger black holes with hyperscaling violation. In that case, we show entropy and temperature are depend on $θ$. In $θ=0$ we see our results are agree with the work of Kim and Yamada. We also construct R-charged black hole with hyperscaling violation and obtain thermodynamics and transport properties.

带有超标度违反的各向异性 Schrödinger 黑洞

Anisotropic Schrödinger black holes with hyperscaling-violation

研究了非最小耦合自相互作用 dilaton 标量的 Einstein-Maxwell 理论在 Schrödinger 背景下的精确解，发现包含黑洞在内的三族构型，并详尽分析了其因果结构、运动学及热力学性质。

Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr{\" o}dinger Equation

The quantization of the superclassical system used in the proof of the index theorem results in a factor of $\hbar^{2}R/8 $ in the Hamiltonian. The path integral expression of the kernel is analyzed up to and including 2-loop order. The existence of the scalar curvature term is confirmed by comparing the linear term in the heat kernel expansion with the 2-loop order terms in the loop expansion.

Schrödinger Holography with and without Hyperscaling Violation

We study the properties of the Schrödinger-type non-relativistic holography for general dynamical exponent z with and without hyperscaling violation exponent θ. The scalar correlation function has a more general form due to general z as well as the presence of θ, whose effects also modify the scaling dimension of the scalar operator. We propose a prescription for minimal surfaces of this "codimension 2 holography," and demonstrate the (d-1) dimensional area law for the entanglement entropy from (d+3) dimensional Schrödinger backgrounds. Surprisingly, the area law is violated for d+1 < z < d+2,…

Quasiperiodic Solutions of the Fibre Optics Coupled Nonlinear Schr{ö}dinger Equations

We consider travelling periodical and quasiperiodical waves in single mode fibres, with weak birefringence and under the action of cross-phase modulation. The problem is reduced to the ``1:2:1" integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasiperiodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasiperiodic solutions to ell…

On the Schr{ö}dinger-Newton equation and its symmetries: a geometric view

The \SN (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over $(\d+1)$-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schrödinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent $z=(\d+2)/3$.