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Related Concept Videos

Gauss's Law01:07

Gauss's Law

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Gauss's Law: Problem-Solving01:10

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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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Equilibrium Conditions for a Particle01:23

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Gauss's Law: Spherical Symmetry01:26

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Equilibration via Gaussification in Fermionic Lattice Systems.

M Gluza1, C Krumnow1, M Friesdorf1

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

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|November 19, 2016
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Summary
This summary is machine-generated.

Non-Gaussian states rapidly equilibrate to Gaussian states in certain quantum systems. This finding, based on correlation clustering and delocalizing transport, offers new insights into quantum dynamics and cold atom experiments.

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Statistical mechanics

Background:

  • Understanding the dynamics of quantum systems far from equilibrium is crucial.
  • Noninteracting fermionic Hamiltonians are fundamental models in condensed matter physics.
  • The process of equilibration and the emergence of Gaussian states are key phenomena.

Purpose of the Study:

  • To investigate the conditions under which non-Gaussian states equilibrate to Gaussian states.
  • To analyze the dynamics of quadratic noninteracting fermionic Hamiltonians.
  • To provide a rigorous proof for the convergence to a generalized Gibbs ensemble.

Main Methods:

  • Utilizing two core assumptions: clustering of correlations in the initial state and delocalizing transport in the Hamiltonian.
  • Developing a general argument applicable to pure and mixed initial states.
  • Applying the framework to various lattice systems and spin systems.

Main Results:

  • Proving that non-Gaussian initial states become locally indistinguishable from fermionic Gaussian states in a controlled time.
  • Demonstrating that this relaxation dynamics follows a power-law independent of system size.
  • Establishing rigorously proven instances of convergence to a generalized Gibbs ensemble.

Conclusions:

  • The study provides a powerful framework for understanding equilibration in quantum many-body systems.
  • The results offer a new intuition for quantum dynamics, applicable to diverse systems including cold atoms in optical lattices.
  • This work bridges theoretical insights with experimental relevance in quantum simulations.