Behavior of entanglement entropy near periodic orbits in a hamiltonian dynamical system

2021 ◽  
Author(s):  
Paul Bracken
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Entanglement Entropy ◽  
Asymptotic Region ◽  
Space Partitioning ◽  
Dynamical Entropy ◽  
Common Limit ◽  
Deep Relationship ◽  
Entropy Growth

Entanglement entropy growth is studied under a form of dynamics that is based on iteration. This approach allows the investigation of the role of decoherence in producing increases of entropy. This has important consequences as far as the study of decoherence is concerned. It is indicated that results are generally independent of Hilbert space partitioning. It is seen that a deep relationship between classical dynamical entropy and the growth of entanglement entropy exists in this kind of model. The former acts to bound the latter and in the asymptotic region, they tend to a common limit.

scholarly journals Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models

2019 ◽  
Vol 100 (22) ◽  
Author(s):  
Oskar Schnaack ◽  
Niklas Bölter ◽  
Sebastian Paeckel ◽  
Salvatore R. Manmana ◽  
Stefan Kehrein ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Lattice Models ◽  
Space Partitioning ◽  
Quantum Lattice

scholarly journals Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Feng Zhang ◽  
Niladri Gomes ◽  
Noah F. Berthusen ◽  
Peter P. Orth ◽  
Cai-Zhuang Wang ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Quantum Chemical Calculations ◽  
Quantum Chemical ◽  
Space Partitioning

scholarly journals Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Dimensional Lattice ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional ◽  
Diffusion Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.

Stockholder projector analysis: A Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

2012 ◽  
Vol 136 (1) ◽  
pp. 014107 ◽  
Author(s):  
Diederik Vanfleteren ◽  
Dimitri Van Neck ◽  
Patrick Bultinck ◽  
Paul W. Ayers ◽  
Michel Waroquier
Keyword(s):  
Hilbert Space ◽  
Density Matrix ◽  
Electron Density ◽  
Space Partitioning ◽  
Electron Density Matrix ◽  
Orthogonal Projectors

scholarly journals Greedy measurement selection for state estimation

2018 ◽  
Author(s):  
J. Nichols ◽  
Albert Cohen ◽  
Peter Binev ◽  
Olga Mula
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
High Dimensional ◽  
Dimensional Vector ◽  
Physical Processes ◽  
Linear Measurements ◽  
Measurement Selection ◽  
Selection For ◽  
Unknown Solution

Parametric PDEs of the general form $$ \mathcal{P}(u,a)=0 $$ are commonly used to describe many physical processes, where $\mathcal{P}$ is a differential operator, a is a high-dimensional vector of parameters and u is the unknown solution belonging to some Hilbert space V. Typically one observes m linear measurements of u(a) of the form $\ell_i(u)=\langle w_i,u \rangle$, $i=1,\dots,m$, where $\ell_i\in V'$ and $w_i$ are the Riesz representers, and we write $W_m = \text{span}\{w_1,\ldots,w_m\}$. The goal is to recover an approximation $u^*$ of u from the measurements. The solutions u(a) lie in a manifold within V which we can approximate by a linear space $V_n$, where n is of moderate dimension. The structure of the PDE ensure that for any a the solution is never too far away from $V_n$, that is, $\text{dist}(u(a),V_n)\le \varepsilon$. In this setting, the observed measurements and $V_n$ can be combined to produce an approximation $u^*$ of u up to accuracy $$ \Vert u -u^*\Vert \leq \beta^{-1}(V_n,W_m) \, \varepsilon $$ where $$ \beta(V_n,W_m) := \inf_{v\in V_n} \frac{\Vert P_{W_m}v\Vert}{\Vert v \Vert} $$ plays the role of a stability constant. For a given $V_n$, one relevant objective is to guarantee that $\beta(V_n,W_m)\geq \gamma >0$ with a number of measurements $m\geq n$ as small as possible. We present results in this direction when the measurement functionals $\ell_i$ belong to a complete dictionary.

scholarly journals Information dynamics in a model with Hilbert space fragmentation

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Dominik Hahn ◽  
Paul A. McClarty ◽  
David J. Luitz
Keyword(s):  
Hilbert Space ◽  
Entanglement Entropy ◽  
Long Distance ◽  
Information Dynamics ◽  
Geometrically Frustrated ◽  
Equilibrium Dynamics ◽  
Maximum Value ◽  
Far From Equilibrium ◽  
Quench Dynamics ◽  
Frustrated Spin

The fully frustrated ladder – a quasi-1D geometrically frustrated spin one half Heisenberg model – is non-integrable with local conserved quantities on rungs of the ladder, inducing the local fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

scholarly journals From Information and Quantum Physics to Consciousness and Reality

Sci ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 35
Author(s):  
Peter Verheyen
Keyword(s):  
Quantum Physics ◽  
Entanglement Entropy ◽  
Relativity Theory ◽  
Recent Theory ◽  
Algorithmic Information Theory ◽  
Person Perspective ◽  
The World ◽  
Algorithmic Information ◽  
Role Of Information

How does the world around us work and what is real? This question has preoccupied humanity since its beginnings. From the 16th century onwards, it has periodically been necessary to revise the prevailing worldview—but things became very strange at the beginning of the 20th century with the advent of relativity theory and quantum physics. The current focus is on the role of information, there being a debate about whether this is ontological or epistemological. A theory has recently been formulated in which spacetime and gravity emerges from microscopic quantum information—more specifically from quantum entanglement via entanglement entropy. A recent theory describes the emergence of reality itself through first-person perspective experiences and algorithmic information theory. In quantum physics, perception and observation play a central role. Perception of and interaction with the environment require an exchange of information. Via biochemical projection, information is given an interpretation that is necessary to make life and consciousness possible. The world around us is not at all what it seems.

From Information and Quantum Physics to Consciousness and Reality

2021 ◽  
Author(s):  
Peter Verheyen
Keyword(s):  
Quantum Physics ◽  
Entanglement Entropy ◽  
Relativity Theory ◽  
Role Perception ◽  
Algorithmic Information Theory ◽  
Person Perspective ◽  
The World ◽  
Algorithmic Information ◽  
Role Of Information

How does the world around us work and what is real? This question has preoccupied humanity since its beginnings. From the 16th century onwards, it has been periodically necessary to revise the prevailing worldview. But things became very strange at the beginning of the 20th century with the advent of relativity theory and quantum physics. The current focus is on the role of information, there being a debate about whether this is ontological or epistemological. A theory has recently been formulated in which spacetime and gravity emerges from microscopic quantum information, more specifically from quantum entanglement via entanglement entropy. A latest theory describes the emergence of reality itself through first-person perspective experiences and algorithmic information theory. In quantum physics, perception and observation play a central role. Perception, interaction with the environment, requires an exchange of information. Via biochemical projection, information is given an interpretation that is necessary to make life and consciousness possible. The world around us is not at all what it seems.

Narcissism Dynamics

2021 ◽  
Author(s):  
Elizabeth A. Edershile ◽  
Aidan G.C. Wright
Keyword(s):  
Dynamical System ◽  
Empirical Research ◽  
Empirical Work ◽  
Theoretical Work ◽  
Self Esteem ◽  
Dynamic Processes ◽  
Cross Sectional ◽  
Complex Dynamical System ◽  
Antagonistic Behavior

The scientific study of narcissism has accelerated in recent years. However, this literature has primarily been cross-sectional and descriptive in nature, making it difficult to integrate with theories of narcissism, which instead emphasize various dynamics. Theoretical work construes narcissism as a complex dynamical system with processes that interact to contribute to narcissism expression and maintenance. We begin by reviewing theoretical accounts of narcissism and what they suggest about dynamic processes. We then review research that examines processes associated with narcissism in naturalistic settings. Integrating clinical theories with empirical work, we highlight remaining tensions in the field and discuss major conceptual considerations. For example, we discuss the role of entitlement and antagonistic behavior within narcissism and the need to identify the temporal ordering of various processes (e.g., self-esteem fluctuations and fluctuations in grandiosity and vulnerability). In light of limitations of the existing literature, we then discuss methodological barriers that currently limit the ability to fully align empirical research with theorized processes within narcissism.

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