scholarly journals Time dependent dark energy and the thermodynamics of many-body systems

2020 ◽  
Vol 29 ◽  
pp. 100596
Author(s):  
Behnam Pourhassan ◽  
Sudhaker Upadhyay
Keyword(s):  
Dark Energy ◽  
Time Dependent ◽  
Many Body ◽  
Many Body Systems

scholarly journals KEY CONCEPTS IN TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY

2001 ◽  
Vol 15 (14) ◽  
pp. 1969-2023 ◽  
Author(s):  
ROBERT VAN LEEUWEN
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Time Dependent ◽  
Response Functions ◽  
Many Body ◽  
Functional Theory ◽  
Key Concepts ◽  
Initial States ◽  
Many Body Systems ◽  
Dependent Density

We give an overview of the underlying concepts of time-dependent density-functional theory. The basic relations between densities, potentials and initial states, for time-dependent many-body systems are discussed. We obtain some new results concerning the invertability of response functions. Some fundamental difficulties associated with the time-dependent action principle are discussed and we show how these difficulties can be resolved by means of the Keldysh formalism.

scholarly journals Fast converging path integrals for time-dependent potentials: II. Generalization to many-body systems and real-time formalism

2011 ◽  
Vol 2011 (03) ◽  
pp. P03005 ◽  
Author(s):  
Antun Balaž ◽  
Ivana Vidanović ◽  
Aleksandar Bogojević ◽  
Aleksandar Belić ◽  
Axel Pelster
Keyword(s):  
Real Time ◽  
Path Integrals ◽  
Time Dependent ◽  
Many Body ◽  
Time Formalism ◽  
Many Body Systems ◽  
Real Time Formalism

scholarly journals Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems

2021 ◽  
Author(s):  
Tong Jiang ◽  
Jiajun Ren ◽  
Zhigang Shuai
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Time Dependent ◽  
Matrix Product ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Spectral Functions ◽  
Matrix Product States ◽  
Many Body Systems ◽  
First Time

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

Strongly correlated quantum walks with a 12-qubit superconducting processor

Science ◽  
2019 ◽  
Vol 364 (6442) ◽  
pp. 753-756 ◽  
Author(s):  
Zhiguang Yan ◽  
Yu-Ran Zhang ◽  
Ming Gong ◽  
Yulin Wu ◽  
Yarui Zheng ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Walks ◽  
Superconducting Qubits ◽  
Time Dependent ◽  
Strongly Correlated ◽  
Superconducting Qubit ◽  
Many Body ◽  
Universal Quantum ◽  
Many Body Systems

Quantum walks are the quantum analogs of classical random walks, which allow for the simulation of large-scale quantum many-body systems and the realization of universal quantum computation without time-dependent control. We experimentally demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. First, in one-photon quantum walks, we observed the propagation of the density and correlation of the quasiparticle excitation of the superconducting qubit and quantum entanglement between qubit pairs. Second, when implementing two-photon quantum walks by exciting two superconducting qubits, we observed the fermionization of strongly interacting photons from the measured time-dependent long-range anticorrelations, representing the antibunching of photons with attractive interactions. The demonstration of quantum walks on a quantum processor, using superconducting qubits as artificial atoms and tomographic readout, paves the way to quantum simulation of many-body phenomena and universal quantum computation.

scholarly journals Spectral decoupling in many-body quantum chaos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jordan Cotler ◽  
Nicholas Hunter-Jones
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Energy Eigenvalue ◽  
Time Dependent ◽  
Late Time ◽  
Many Body ◽  
Many Body Systems

Abstract We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon “spectral decoupling”, which signifies a dynamical onset of random matrix theory in correlation functions. A key diagnostic of spectral decoupling is k-invariance, which we refine and study in detail. Particular emphasis is placed on the role of symmetries, and connections between k-invariance, scrambling, and OTOCs. Disordered Pauli spin systems, as well as the SYK model and its variants, provide a rich source of disordered quantum many-body systems with varied symmetries, and we study k-invariance in these models with a combination of analytics and numerics.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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