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Gauss's Law01:07

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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 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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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: 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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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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Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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System-bath entanglement theorem with Gaussian environments.

Peng-Li Du1, Yao Wang1, Rui-Xue Xu1

  • 1Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei, Anhui 230026, China.

The Journal of Chemical Physics
|January 24, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a system-bath entanglement theorem for Gaussian environments, linking composite and local entangled response functions. This advances quantum dissipation theories by enabling system-bath entanglement analysis.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Condensed matter physics

Background:

  • Quantum systems are often influenced by their environment (bath).
  • Understanding system-bath interactions is crucial for quantum dynamics.
  • Quantifying entanglement between system and bath is challenging.

Purpose of the Study:

  • To establish a general theorem for system-bath entanglement in Gaussian environments.
  • To connect entangled response functions of composite systems to local ones.
  • To enable evaluation of system-bath entanglement within existing quantum dissipation theories.

Main Methods:

  • Development of the "system-bath entanglement theorem."
  • Validation using the exact dissipaton-equation-of-motion approach.
  • Numerical demonstrations on spin-boson systems with Fano interference spectroscopies.

Main Results:

  • The system-bath entanglement theorem is established for arbitrary systems and Gaussian baths.
  • The theorem relates composite entangled response functions to local system response functions.
  • The theorem's validity is confirmed through direct evaluation and numerical examples.

Conclusions:

  • The established theorem provides a powerful tool for analyzing system-bath entanglement.
  • This work extends the applicability of quantum dissipation theories to entanglement properties.
  • The findings facilitate deeper understanding of quantum correlations in complex systems.