Anhang VII Die Wigner-Transformation

2020 ◽  
pp. 2397-2428
Keyword(s):  
Wigner Transformation

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

Quantum Gel'fand-Levitan method as a generalized Jordan-Wigner transformation

1980 ◽  
Vol 92 (1-2) ◽  
pp. 144-148 ◽  
Author(s):  
Dennis B. Creamer ◽  
H.B. Thacker ◽  
David Wilkinson
Keyword(s):  
Wigner Transformation

The Wigner transformation is of finite order

1987 ◽  
Vol 28 (10) ◽  
pp. 2390-2392 ◽  
Author(s):  
Joseph C. Várilly ◽  
José M. Gracia‐Bondía
Keyword(s):  
Finite Order ◽  
Wigner Transformation

The Image Watermarking against Shearing Based on Dopplerlet Transformation

2011 ◽  
Vol 181-182 ◽  
pp. 276-280
Author(s):  
Ming Hui Deng ◽  
Wen Zhe Li ◽  
Qi Chen Li
Keyword(s):  
Spatial Frequency ◽  
Dimensional Space ◽  
Image Watermarking ◽  
Time Windows ◽  
Geometric Distortion ◽  
Frequency Change ◽  
Two Dimensional ◽  
Frequency Distributions ◽  
Chirp Signals ◽  
Wigner Transformation

In this paper, a robust image watermarking method in two-dimensional space/spatial-frequency distributions domain is proposed which is robust against geometric distortion. This watermarking is detected by a linear frequency change. The dopplerlet transformation is used to detect the watermark. The chirp signals are used as watermarks and this type of signals is resistant to all stationary filtering methods and exhibits geometrical symmetry. In the two-dimensional Radon-Wigner transformation domain, the chirp signals used as watermarks change only its position in space/spatial-frequency distribution, after applying linear geometrical attack, such as scale rotation and cropping. But the two-dimensional Radon-Wigner transformation needs too much difficult computing. So the image is put into a series of 1D signal by choosing scalable local time windows. The watermark embedded in the dopplerlet transformation domain. The watermark thus generated is invisible and performs well in StirMark test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.

One-dimensional quantum spin heterojunction as a thermal switch

2016 ◽  
Vol 30 (07) ◽  
pp. 1650027
Author(s):  
Chuan-Jing Yang ◽  
Li-Hui Jin ◽  
Wei-Jiang Gong
Keyword(s):  
Thermal Transport ◽  
Structural Parameters ◽  
Finite Size ◽  
Quantum Spin ◽  
Spin Interaction ◽  
Heat Current ◽  
Spin Hamiltonian ◽  
One Dimensional ◽  
Thermal Switch ◽  
Wigner Transformation

We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.

Thermal Entanglement Entropy Signature of Spin-Peierls Transition in Dimerized Isotropic XY Chain with Multi-Spin Interactions

2014 ◽  
Vol 1021 ◽  
pp. 46-51
Author(s):  
Hai Lin Huang ◽  
Lin Jie Ding ◽  
Zhao Yu Sun
Keyword(s):  
Green's Function ◽  
Finite Temperature ◽  
Function Theory ◽  
Critical Phenomenon ◽  
Entanglement Entropy ◽  
Spin Interaction ◽  
Thermal Entanglement ◽  
Spin Interactions ◽  
Wigner Transformation ◽  
Peierls Transition

The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (SP) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize theSPtransition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.

Application of Mean-Field Jordan–Wigner Transformation to Antiferromagnet System

2008 ◽  
Vol 50 (1) ◽  
pp. 243-247
Author(s):  
Li Jia-Liang ◽  
Lei Shu-Guo ◽  
Jiang Yu-Chi
Keyword(s):  
Mean Field ◽  
Wigner Transformation

Superfluidity of the Lattice Anyon Gas

1989 ◽  
Vol 03 (12) ◽  
pp. 1965-1995 ◽  
Author(s):  
Eduardo Fradkin
Keyword(s):  
Quantum Hall ◽  
Goldstone Mode ◽  
Two Dimensional ◽  
Hall Conductance ◽  
Dimensional Lattice ◽  
Quantum Hall Systems ◽  
Wigner Transformation ◽  
Topological Invariance ◽  
Quantum Hall System ◽  
Chern Simons

I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

Sign in / Sign up

Export Citation Format

Share Document