scholarly journals Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

2021 ◽  
Vol 36 (35) ◽  
Author(s):  
MuSeong Kim ◽  
Mi-Ra Hwang ◽  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Temperature Region ◽  
Thermal State ◽  
Generalized Uncertainty Principle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Large Temperature ◽  
Von Neumann

The Rényi and von Neumann entropies of thermal state in generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of GUP parameter [Formula: see text]. While the von Neumann entropy with [Formula: see text] exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes a decreasing behavior at large temperature region. As a result, for the case of [Formula: see text], the von Neumann entropy is maximized at the finite temperature [Formula: see text]. The Rényi entropy [Formula: see text] with nonzero [Formula: see text] also exhibits similar behavior at large temperature region. In this region, the Rényi entropy exhibits a decreasing behavior with increasing temperature. The decreasing rate becomes larger when the order of the Rényi entropy is smaller.

scholarly journals The generalized and extended uncertainty principles and their implications on the Jeans mass

2019 ◽  
Vol 488 (1) ◽  
pp. L69-L74 ◽  
Author(s):  
H Moradpour ◽  
A H Ziaie ◽  
S Ghaffari ◽  
F Feleppa
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Newtonian Gravity ◽  
Uncertainty Principles ◽  
Temperature Relation ◽  
Heisenberg Uncertainty Principle ◽  
Extended Uncertainty

ABSTRACT The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy–temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism that lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

scholarly journals Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Olalla Castro-Alvaredo
Keyword(s):  
Field Theory ◽  
Bessel Functions ◽  
Entanglement Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Numerical Work ◽  
Von Neumann ◽  
Twist Fields ◽  
Toda Field Theory

In this letter we study the exponentially decaying corrections to saturation of the second Rényi entropy of one interval of length \ellℓ in minimal E_8E8 Toda field theory. It has been known for some time that the entanglement entropy of a massive quantum field theory in 1+1 dimensions saturates to a constant value for m_1\ell\gg 1m1ℓ≫1 where m_1m1 is the mass of the lightest particle in the spectrum. Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there are exponentially decaying corrections to this behaviour which are characterized by Bessel functions with arguments proportional to m_1\ellm1ℓ. For the von Neumann entropy the leading correction to saturation takes the precise universal form -\frac{1}{8}K_0(2m_1\ell)−18K0(2m1ℓ) whereas for the Rényi entropies leading corrections which are proportional to K_0(m_1\ell)K0(m1ℓ) are expected. Recent numerical work by Pálmai for the second Rényi entropy of minimal E_8E8 Toda has identified next-to-leading order corrections which decay as e^{-2m_1\ell}e−2m1ℓ rather than the expected e^{-m_1\ell}e−m1ℓ. In this paper we investigate the origin of this result and show that it is incorrect. An exact form factor computation of correlators of branch point twist fields reveals that the leading corrections are proportional to K_0(m_1 \ell)K0(m1ℓ) as expected.

scholarly journals Information Dynamic Correlation of Vibration in Nonlinear Systems

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 56
Author(s):  
Zhe Wu ◽  
Guang Yang ◽  
Qiang Zhang ◽  
Shengyue Tan ◽  
Shuyong Hou
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
System Dynamics ◽  
Mechanical Systems ◽  
Modal Identification ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Identification System ◽  
Von Neumann

In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

scholarly journals The extended uncertainty principle inspires the Rényi entropy

2019 ◽  
Vol 127 (6) ◽  
pp. 60006 ◽  
Author(s):  
H. Moradpour ◽  
C. Corda ◽  
A. H. Ziaie ◽  
S. Ghaffari
Keyword(s):  
Uncertainty Principle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Extended Uncertainty

scholarly journals Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Pasquale Bosso ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Exact Form ◽  
Ladder Operators ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

AbstractSeveral models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

scholarly journals Entanglement entropy from TFD entropy operator

2021 ◽  
Vol 36 (13) ◽  
pp. 2150092
Author(s):  
M. Dias ◽  
Daniel L. Nedel ◽  
C. R. Senise
Keyword(s):  
Analytic Continuation ◽  
Moduli Space ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Expected Value ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Von Neumann

In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the Rényi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.

scholarly journals Some Implications of Two Forms of the Generalized Uncertainty Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammed M. Khalil
Keyword(s):  
Hydrogen Atom ◽  
Quantum Gravity ◽  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Standard Uncertainty ◽  
Minimum Length ◽  
Length Scale ◽  
Minimum Length Scale ◽  
Lorentz Force Law

Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of the GUP and calculate their implications on the energy of the harmonic oscillator and the hydrogen atom more accurately than previous studies. In addition, we show how the GUP modifies the Lorentz force law and the time-energy uncertainty principle.

scholarly journals Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space

2016 ◽  
Vol 94 (1) ◽  
pp. 139-146 ◽  
Author(s):  
Saurya Das ◽  
Matthew P.G. Robbins ◽  
Mark A. Walton
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Uncertainty Principles ◽  
Marginal Probability ◽  
Wigner Functions ◽  
Simple Harmonic Oscillator ◽  
Probability Densities

We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.

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