Relativistic effects in many-body systems of finite size, internal structure, and internal motions. II. The determination of the inertial and rest masses of binary stars

1981 ◽  
Vol 13 (5) ◽  
pp. 487-493 ◽  
Author(s):  
N. Spyrou
Keyword(s):  
Internal Structure ◽  
Binary Stars ◽  
Finite Size ◽  
Relativistic Effects ◽  
Many Body ◽  
Internal Motions ◽  
Many Body Systems

The Right Variables and Natural Kinds

2021 ◽  
pp. 120-136
Author(s):  
Robert W. Batterman
Keyword(s):  
Correlation Function ◽  
Natural Kinds ◽  
Scientific Methodology ◽  
Many Body ◽  
Material Parameters ◽  
Fluctuation Dissipation ◽  
Hydrodynamic Correlation ◽  
Many Body Systems ◽  
The Right

This chapter argues that mesoscale parameters (order parameters and material parameters) are the natural variables by which we can characterize and understand lawful behaviors of many-body systems. It engages in a debate about whether the determination of natural kinds flows from metaphysical considerations about fundamentality and carving nature at its joins or from goal oriented aims of ones scientific methodology. The chapter argues for a scientific determination of the natural variables (at least in the case of many-body systems) based on the previous discussions of the hydrodynamic, correlation function approach. The Fluctuation-Dissipation theorem provides a justification for taking the mesoscale variables and parameters to be natural kinds.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

2018 ◽  
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals What Kind of Insight Provide Analytical Solutions of Quantum Models?

2020 ◽  
pp. 5-6
Author(s):  
Daniel Braak
Keyword(s):  
System Size ◽  
Quantum Model ◽  
Many Body ◽  
Hamilton Operator ◽  
Asymptotic Dynamics ◽  
Many Body Systems ◽  
Liouville Integrable ◽  
Insight Into ◽  
Spectral Determinant

Abstract There are several concepts of what constitutes the analytical solution of a quantum model, as opposed to the mere “numerically exact” one. This applies even if one considers only the determination of the discrete spectrum of the corresponding Hamiltonian, setting aside such important questions as the asymptotic dynamics for long times. In the simplest case, the spectrum can be given in closed form, the eigenvalues $$E_{j}, j=0,\ldots ,N\le \infty $$ read $$E_{j} =f(j,\{p_{k}\})$$, where f is a known function of the label $$j\in \mathbb {N}_{0}$$ and the $$\{p_k\}$$ are a set of numbers parameterizing the Hamilton operator. This kind of solution exists only in cases where the classical limit of the model is Liouville-integrable. Some quantum-mechanical many-body systems allow the determination of the spectrum in terms of auxiliary parameters $$[\{k_j\},\{n_l\}]$$ as $$E(\{n_l\}) = f(\{k_{j}(\{n_{l}\})\})$$ where the $$\{k_{j}(\{n_{l}\})\}$$ satisfy a coupled set of transcendental equations, following from a certain ansatz for the eigenfunctions. These systems (integrable in the sense of Yang-Baxter (Eckle 2019)) may have a Hilbert space dimension growing exponentially with the system size L, i.e., $$N\sim e^{L}$$. The simple enumeration of the energies with the label j is replaced by the multi-index $$\{n_{l}\}$$. Although no priori knowledge about the spectrum is available, its statistical properties can be computed exactly (Berry and Tabor 1977). Other integrable and also non-integrable models exist where N depends polynomially on L and the energies $$E_j$$ are the zeroes of an analytically computable transcendental function, the so-called G-function $$G(E,\{p_k\})$$ (Braak 2013a, 2016), which is proportional to the spectral determinant. Although no closed formula for $$E_j$$ as function of the index j exists, detailed qualitative insight into the distribution of the eigenvalues can be obtained (Braak 2013b). Possible applications of these concepts to information compression and cryptography are outlined.

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.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems
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