Related Experiment Video
Updated: May 3, 2026
07:45
Quasi-light Storage for Optical Data Packets
Published on: February 6, 2014
10.1K
Compression algorithm for discrete light-cone quantization.
Xiao Pu1, Sophia S Chabysheva1, John R Hiller1
1Department of Physics, University of Minnesota-Duluth, Duluth, Minnesota 55812, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
Summary
We adapted a compression algorithm for spin lattice Hamiltonians to light-front field theories. This method efficiently represents and compresses Hamiltonian eigenvectors using singular value decomposition for quantum field theory calculations.
Area of Science:
- Quantum Field Theory
- Computational Physics
Background:
- Spin lattice Hamiltonians are complex systems.
- Efficiently representing Hamiltonian eigenvectors is crucial for solving quantum field theory problems.
Purpose of the Study:
- To adapt a known compression algorithm for spin lattice Hamiltonians.
- To apply this algorithm to light-front field-theoretic Hamiltonians.
Main Methods:
- Adapted the Weinstein, Auerbach, and Chandra compression algorithm.
- Used discrete light-cone quantization (DLCQ) for matrix representation.
- Represented eigenvectors using singular value decomposition (SVD) of 2D arrays.
- Compressed eigenvectors via SVD truncation.
- Decomposed the rank-four Hamiltonian tensor into factorized matrices.
Main Results:
- Successfully adapted the compression algorithm for light-front Hamiltonians.
- Demonstrated the method's utility in a model theory.
- Efficient representation and compression of Hamiltonian eigenvectors achieved.
Conclusions:
- The adapted algorithm provides an efficient method for handling Hamiltonian eigenvectors in light-front field theory.
- Singular value decomposition offers a powerful tool for compressing quantum field theory data.
- This approach facilitates computational solutions for complex field theory problems.
Related Concept Videos
01:24Convolution: Math, Graphics, and Discrete Signals
1.3K
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
1.3K
01:20Downsampling
872
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
872
01:16Confocal Fluorescence Microscopy
16.0K
Confocal microscopy is an advanced microscopic technique. The prime advantage of the confocal microscope over other microscopy techniques is its ability to block the out-of-focus light from the illuminated samples using pinholes. It is widely used with fluorescence optics to obtain high-resolution, sharp contrast images. Unlike optical microscopes, confocal microscopes use a focused beam of light laser to scan the entire sample surface at different z-planes. These microscopes are, therefore,...
16.0K
01:26Discrete-time Fourier transform
1.5K
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
One of the notable...
1.5K
01:15Discrete Fourier Transform
1.3K
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
1.3K
01:26Linear Approximation in Frequency Domain
502
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
502