We probe the low-temperature behavior of a system of quantum bouncers as a theoretical model for ultracold neutrons within a low energy modified version of the standard quantum mechanics, due to the gravitational effects. Working in one dimension, the energy spectrum and bound states of a deformed quantum bouncer are obtained using the first-order WKB approximation, granted the very low energy regime of the particle. In this manner, we can study energy levels of a system of ultracold neutrons as an informative probe towards exploring the low energy manifestation of semi-classical quantum gravitational effects. Our calculated energy levels of ultracold neutrons are in accordance with the observed energy levels, as obtained in the famous Nesvizhevsky \emph{et al.} experiment, with a negative constant deformation, as dependent on the deformation parameter. In advance, we tackle modified thermodynamics of a system of quantum bouncers in the infrared regime via an ensemble theory both in one dimension and also three dimensions, to seek for any trace of an effective, thermodynamic dimensional reduction in this low energy regime of semi-classical quantum gravity. While the issue of dimensional reduction has been essentially assigned to the high energy regime, here we show that there is a trace of an effective, thermodynamic dimensional reduction in infrared regime with one important difference: in the high energy regime, the dimensional reduction effectively occurs from $D=3$ to $D=1$, but here, in this low energy regime, there is a trace of thermodynamic dimensional reduction from $D=3$ to $D=2$.
We compute the Hagedorn temperature of $μT \bar T + \varepsilon_+ J \bar T + \varepsilon_-T \bar J$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of $μ$, $\varepsilon_+$, and $\varepsilon_-$ for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed $AdS_3 \times S^1 \times T^3 \times S^3$ using holographic methods. We identify black hole configurations whose thermodynamics …
We study the thermodynamic properties of massless Dirac fermions in graphene under a uniform magnetic field and Rashba spin-orbit coupling with a $q-$deformed Heisenberg algebra calculus. The thermodynamic functions such as the Helmholtz free energy, total energy, entropy and heat capacity are obtained by using an approach based on the zeta function and Euler-Maclaurain formula. These functions will be numerically examined for different values of $η={1\over i}\ln(q)$. In particular, the heat capacity in the presence of deformation, all curves coincide and reach the fixed value $C=6K_B$ three t…
In this paper we study the thermodynamics of black branes with a modulated complex scalar in the context of bulk and boundary theories. The modulation induces inhomogeneity to the dual field theory, anisotropic pressure, and brane charge to the bulk geometry. The first law of thermodynamics and the Smarr relation are obtained using the off-shell ADT and the reduced action formalisms. We discuss the prescription for the mass of black branes, which relies on relevant and marginal deformations in the dual field theory. One of the cases is the gravity dual to a ABJM model with a sinusoidal mass fu…
In this work, we study the effect of $κ$-deformed space on the thermodynamic quantities, this are find through the holographic renormalization that provide the free energy, which is fundamental to derive the another thermodynamic quantities. For this scenario we consider an charged AdS$_{4}$ black hole for an Einstein-Maxwell model where the derivative quadrivector is replaced by a deformed version inspired in Kaniadakis statistics. Besides, we extract the transport coefficient know as electrical conductivity.
We show that the $T \bar T$ deformation of conformal field theories whose entropy grows as $S(E) \sim E^γ$ for $γ> 1/2$ exhibits negative specific heat in its microcanonical thermodynamic function $S({\cal E})$. We analyze the large $N$ symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as $S({\cal E})$ and ${\cal E}(T)$. The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.
We study various aspects of the mass deformed SYK model which can escape the interiors of pure boundary state black holes. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of…
We have presented a set of laws of entanglement thermodynamics for $T\bar{T}$-deformed CFTs and in general for $T^2$-deformed field theories. In particular, the first law of this set, states that although we are dealing with a non-trivial deformed theory, the change of the entanglement entropy is simply translated to the change of the bending energy of the entangling surface. We interpret this energy as the energy of decomposition. Probing the whole spectrum of the deformed theory, a second law also results, which suggests an inequality that the first law is derived from its saturation limit. …
In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $J\bar{T}$ deformation and deformation by a general linear combination of $T\bar{T}$ and $J\bar{T}$ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of…
We review our recent work [arXiv:2009.10759] where we studied the chaotic property of the two coupled Sachdev-Ye-Kitaev systems exhibiting a Hawking-Page like phase transition. By computing the out-of-time-ordered correlator in the large N limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous fall-off at the phase transition temperature. Hence in this model the Hawking-Page like transition is correlated with a transition in chaoticity, as expected from the relation between a black hole geometry and the chaotic behavior in the dual fiel…
It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times…
In this thesis we discuss how one can derive the quantum spectral curve for the $η$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS$_5 \times $S$^5$ superstring, like the Heisenberg xxz spin chain is a trigonometric version of the xxx spin chain. Our derivation starts from the ground-state thermodynamic Bethe ansatz equations and discusses the construction of both the undeformed and the $η$-deformed quantum spectral curve. We reformulate it firs…
Considering Verlinde's entropic gravity proposal, we focus the effects of fermionic $q$ deformation on the Einstein's field equations and Friedmann equations. For this purpose, we represent the thermodynamical properties of the deformed fermion gas model in two-dimensional space. To describe the behavior of the quantum black holes, deformed Einstein field equations are derived with the help of deformed entropy function. Moreover, deformed Friedmann equations are investigated by using Friedmann-Robertson-Walker (FRW) metric. We also present the effective ones of the energy density, the pressure…
Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes
Institute of Mathematics, University of the Punjab（旁遮普大学数学研究所）；Faculty of Symbiotic Systems Science, Fukushima University（福岛大学共生系统科学学院）；Department of Mathematics, College of Science, King Saud University（国王沙特大学理学院数学系）；Department of Mathematics, Quaid-i-Azam University（真纳大学数学系）；Research Center of Astrophysics and Cosmology, Khazar University（哈扎尔大学天体物理学与宇宙学研究中心）
