scholarly journals Spectral form factors and late time quantum chaos

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Junyu Liu
Keyword(s):  
Quantum Chaos ◽  
Form Factors ◽  
Late Time ◽  
Spectral Form ◽  
Time Quantum

scholarly journals Early-time and late-time quantum chaos

2020 ◽  
Vol 35 (18) ◽  
pp. 2050082
Author(s):  
Chen-Te Ma
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Quantum Chaos ◽  
Early Time ◽  
Late Time ◽  
Time Study ◽  
Spectral Form ◽  
Numerical Result ◽  
Direct Extension ◽  
Time Quantum

We show the relation between the Heisenberg averaging of regularized 2-point out-of-time ordered correlation function and the 2-point spectral form factor in bosonic quantum mechanics. The generalization to all even-point is also discussed. We also do the direct extension from the bosonic quantum mechanics to the noninteracting scalar field theory. Finally, we find that the coherent state and large-[Formula: see text] approaches are useful in the late-time study. We find that the computation of the coherent state can be simplified by the Heisenberg averaging. Therefore, this provides a simplified way to probe the late-time quantum chaos through a coherent state. The large-[Formula: see text] result is also comparable to the [Formula: see text] numerical result in the large-[Formula: see text] quantum mechanics. This can justify that large-[Formula: see text] technique in bosonic quantum mechanics can probe the late time, not the early time. Because the quantitative behavior of large-[Formula: see text] can be captured from the [Formula: see text] numerical result, the realization in experiments should be possible.

scholarly journals Late-time quantum backreaction of a very light nonminimally coupled scalar

2016 ◽  
Vol 94 (8) ◽  
Author(s):  
Dražen Glavan ◽  
Tomislav Prokopec ◽  
Tomo Takahashi
Keyword(s):  
Late Time ◽  
Time Quantum

scholarly journals Late-time quantum radiation by a uniformly accelerated detector in de Sitter spacetime

2018 ◽  
Vol 98 (10) ◽  
Author(s):  
Shumpei Yamaguchi ◽  
Rumi Tatsukawa ◽  
Shih-Yuin Lin ◽  
Kazuhiro Yamamoto
Keyword(s):  
Late Time ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Quantum Radiation ◽  
Time Quantum

scholarly journals Deformations of JT gravity via topological gravity and applications

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Stefan Förste ◽  
Hans Jockers ◽  
Joshua Kames-King ◽  
Alexandros Kanargias
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Form Factors ◽  
Temperature Limit ◽  
Partition Functions ◽  
De Sitter ◽  
Spectral Form ◽  
Kdv Hierarchy ◽  
Topological Gravity ◽  
Perturbative Corrections

Abstract We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition function becomes exact. In this limit we demonstrate that there is a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity with a transition temperature affected by the presence of defects. Furthermore, the calculated spectral form factors show the qualitative behaviour expected for a Hawking-Page phase transition. The considered deformations cause the ramp to be shifted along the real time axis. Finally, we comment on recent results related to conical Weil-Petersson volumes and the analytic continuation to two-dimensional de Sitter space.

scholarly journals Spectral form factor for time-dependent matrix model

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Arkaprava Mukherjee ◽  
Shinobu Hikami
Keyword(s):  
Form Factor ◽  
Matrix Model ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Numerical Evaluation ◽  
Time Dependent ◽  
Spectral Form ◽  
Random Matrix Model ◽  
Large Size ◽  
Analytic Expression

Abstract The quantum chaos is related to a Gaussian random matrix model, which shows a dip-ramp-plateau behavior in the spectral form factor for the large size N. The spectral form factor of time dependent Gaussian random matrix model shows also dip-ramp-plateau behavior with a rounding behavior instead of a kink near Heisenberg time. This model is converted to two matrix model, made of M1 and M2. The numerical evaluation for finite N and analytic expression in the large N are compared for the spectral form factor.

scholarly journals Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Parth Bhargava ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Anurag Mishara ◽  
Sachin Panneer Selvam ◽  
...  
Keyword(s):  
Time Scale ◽  
Quantum Chaos ◽  
Circuit Complexity ◽  
Theoretical Interpretation ◽  
Late Time ◽  
Conformal Time ◽  
Squeezed State ◽  
Acceptable Error ◽  
Cost Functionals ◽  
The Universe

Circuit Complexity, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. Cosine hyperbolic and Exponential models of scale factors. Besides circuit complexity, we use the Out-of-Time Ordered correlation (OTOC) functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible but an exponential rise can be seen in the complexity once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-linearly weighted and geodesic weighted with the OTOC. Furthermore, from the complexity computation obtained from both the cosmological models under consideration and also using the well known Maldacena (M) Shenker (S) Stanford (S) bound on quantum Lyapunov exponent, \lambda\leq 2\pi/\betaλ≤2π/β for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at the late time scale. Finally, we provide a rough estimation of the scrambling time scale in terms of the conformal time.

scholarly journals Thermalization of randomly coupled SYK models

2022 ◽  
Vol 2022 (1) ◽  
pp. 013103
Author(s):  
Ramanjit Sohal ◽  
Laimei Nie ◽  
Xiao-Qi Sun ◽  
Eduardo Fradkin
Keyword(s):  
Effective Temperature ◽  
Matrix Theory ◽  
Late Time ◽  
Spectral Form ◽  
Perfect Agreement ◽  
Random Interactions ◽  
State Dependent ◽  
Rényi Entropies ◽  
Reduced Density ◽  
Renyi Entropies

Abstract We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

scholarly journals The double cone geometry is stable to brane nucleation

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Raghu Mahajan ◽  
Donald Marolf ◽  
Jorge E. Santos
Keyword(s):  
Form Factor ◽  
Quantum Chaos ◽  
Higher Dimensions ◽  
Double Cone ◽  
Spectral Form ◽  
Factorization Problem ◽  
Gauge Gravity ◽  
M Theory ◽  
Gravity Duality ◽  
Probe Brane

Abstract In gauge/gravity duality, the bulk double cone geometry has been argued to account for a key feature of the spectral form factor known as the ramp. This feature is deeply associated with quantum chaos in the dual field theory. The connection with the ramp has been demonstrated in detail for two-dimensional theories of bulk gravity, but it appears natural in higher dimensions as well. In a general bulk theory the double cone might thus be expected to dominate the semiclassical bulk path integral for the boundary spectral form factor in the ramp regime. While other known spacetime wormholes have been shown to be unstable to brane nucleation when they dominate over known disconnected (factorizing) solutions, we argue below that the double cone is stable to semiclassical brane nucleation at the probe-brane level in a variety of string- and M-theory settings. Possible implications for the AdS/CFT factorization problem are briefly discussed.

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