imaginary time
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Author(s):  
Hsiu-Chung Yeh ◽  
Dimitri M Gangardt ◽  
A Kamenev

Abstract We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.


2022 ◽  
Vol 258 ◽  
pp. 04004
Author(s):  
Glòria Montaña

We have developed a self-consistent theoretical approach to study the modification of the properties of heavy mesons in hot mesonic matter which takes into account chiral and heavy-quark spin-flavor symmetries. The heavylight meson-meson unitarized scattering amplitudes in coupled channels incorporate thermal corrections by using the imaginary-time formalism, as well as the dressing of the heavy mesons with the self-energies. We report our results for the ground-state thermal spectral functions and the implications for the excited mesonic states generated dynamically in the heavy-light molecular model. We have applied these to the calculation of meson Euclidean correlators and transport coefficients for D mesons and summarize here our findings.


Author(s):  
Tomohiro Inagaki ◽  
Yamato Matsuo ◽  
Hiromu Shimoji

Abstract We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an S1 in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact S1 spatial direction with a U(1)-valued boundary condition. Thus, we study the model on a $\mathbb {R}^{D-2} \times S^{1} \times S^{1}$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the 1/N expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.


2021 ◽  
Author(s):  
Arif Ullah

Open-chain imaginary-time path-integral sampling approach known with the acronym OPSCF (J. Chem. Phys. 148, 102340 (2018)) is an approach to the calculation of approximate symmetrized quantum time correlation functions. In OPSCF approach, the real time t is treated as a parameter, and therefore for each real time t, a separate simulation on the imaginary time axis is needed to be run, which makes the OPSCF approach quite expensive and as a result, the approach loses the advantage of being a standard path-integral sampling approach. In this study, I propose that the use of OPSCF approach in combination with machine learning can reduce the computational cost by 75% to 90% (depending on the problem at hand). Combining OPSCF approach with ML is very straight forward which gives an upper hand to OPSCF approach over the trajectory-based methods such as the centroid molecular dynamics (CMD) and the ring-polymer molecular dynamics (RPMD).


2021 ◽  
Vol 104 (10) ◽  
Author(s):  
F. T. Brandt ◽  
J. Frenkel ◽  
S. Martins-Filho ◽  
D. G. C. McKeon ◽  
G. S. S. Sakoda

2021 ◽  
pp. 2100114
Author(s):  
Niladri Gomes ◽  
Anirban Mukherjee ◽  
Feng Zhang ◽  
Thomas Iadecola ◽  
Cai‐Zhuang Wang ◽  
...  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Raja Selvarajan ◽  
Vivek Dixit ◽  
Xingshan Cui ◽  
Travis S. Humble ◽  
Sabre Kais

AbstractThe road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as $$O(n^{5}d)$$ O ( n 5 d ) , where n is the bit-length of the number to be factorized and d is the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.


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