scholarly journals Wigner function for SU(1,1)

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 317
Author(s):  
U. Seyfarth ◽  
A. B. Klimov ◽  
H. de Guise ◽  
G. Leuchs ◽  
L. L. Sanchez-Soto
Keyword(s):  
Wigner Function ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Scientific Work ◽  
Potential Usefulness ◽  
Wigner Functions ◽  
Expectation Value ◽  
Parity Operator ◽  
Modern Metrology

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.Dedication: While this manuscript was under review, we learnt with great sadness of the untimely passing of our colleague and friend Jonathan Dowling. Through his outstanding scientific work, his kind attitude, and his inimitable humor, he leaves behind a rich legacy for all of us. Our work on SU(1,1) came as a result of long conversations during his frequent visits to Erlangen. We dedicate this paper to his memory.

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

WIGNER FUNCTION OF PULSED FIELDS RECONSTRUCTED BY DIRECT DETECTION

2011 ◽  
Vol 09 (supp01) ◽  
pp. 39-47
Author(s):  
ALESSIA ALLEVI ◽  
MARIA BONDANI ◽  
ALESSANDRA ANDREONI
Keyword(s):  
Probability Distribution ◽  
Wigner Function ◽  
Beam Splitter ◽  
Direct Detection ◽  
Probability Distributions ◽  
Linear Regime ◽  
Wigner Functions ◽  
Intensity Measurements ◽  
Pulsed Fields

We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

Wigner function and the parity operator

1994 ◽  
Vol 190 (5-6) ◽  
pp. 370-372 ◽  
Author(s):  
Hui Li
Keyword(s):  
Wigner Function ◽  
Parity Operator

AB INITIO CALCULATION OF $^5_\Lambda {\rm He}$ WITH EXPLICIT Σ ADMIXTURE

2003 ◽  
Vol 18 (02n06) ◽  
pp. 139-142
Author(s):  
H. NEMURA ◽  
Y. AKAISHI ◽  
Y. SUZUKI
Keyword(s):  
Ab Initio ◽  
Internal Energy ◽  
Ab Initio Calculation ◽  
Degrees Of Freedom ◽  
Bound State ◽  
Bound State Solution ◽  
Expectation Value ◽  
Variational Calculations ◽  
Energy Expectation ◽  
Energy Expectation Value

Variational calculations for s-shell hypernuclei are performed by explicitly including Σ degrees of freedom. Two sets of YN interactions (D2 and SC97e(S)) are used. The bound-state solution of [Formula: see text] is obtained by using each of YN potentials, and a large energy expectation value of the tensor ΛN - ΣN transition part is found by using the SC97e(S). The internal energy of 4 He subsystem changes a lot by the presence of a Λ particle with the strong tensor ΛN - ΣN transition potential.

scholarly journals Husimi–Wigner representation of chaotic eigenstates

2008 ◽  
Vol 464 (2094) ◽  
pp. 1503-1524 ◽  
Author(s):  
Fabricio Toscano ◽  
Anatole Kenfack ◽  
Andre R.R Carvalho ◽  
Jan M Rost ◽  
Alfredo M Ozorio de Almeida
Keyword(s):  
Hilbert Space ◽  
Coherent State ◽  
Pure State ◽  
Degrees Of Freedom ◽  
Factor Space ◽  
Wigner Functions ◽  
Higher Dimensional ◽  
Wigner Representation ◽  
Quantum Point ◽  
The Individual

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

Wigner Distribution Function for Open Quantum Systems

1997 ◽  
Vol 11 (09n10) ◽  
pp. 391-397 ◽  
Author(s):  
S. Baskoutas
Keyword(s):  
Distribution Function ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Analytical Form ◽  
Dissipative Systems ◽  
Wigner Distribution Function ◽  
Dissipative Tunneling ◽  
Lie Algebraic Structure

Using the modified biorthonormal Heisenberg equations of motion for non-Hermitian (NH) Hamilton operators, in order to imply a consistent Lie-algebraic structure and also the equivalence between the Heisenberg and Schrödinger pictures, we have obtained the analytical form of the Wigner distribution function which is unavoidable complex. Its imaginary part accounts for the influence of additional degrees of freedom, which are always present in the phenomenological representation of dissipative systems through (NH) Hamiltonians. Applications of the above formalism can be found, for instance, in dissipative macroscopic quantum tunneling (MQT) effect for Josephson junctions, and in the dissipative tunneling of trapped atoms in optical crystals.

scholarly journals Open Quantum Dynamics Theory on the Basis of Periodical System-Bath Model for Discrete Wigner Function

2021 ◽  
Author(s):  
Yuki Iwamoto ◽  
Yoshitaka Tanimura
Keyword(s):  
Distribution Function ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Equations Of Motion ◽  
Heat Bath ◽  
Planck Equation ◽  
Mesh Size ◽  
Dynamics Simulation ◽  
Open Quantum

Abstract Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

THEORY OF TOMOGRAPHY FOR THE WIGNER FUNCTION OF TRIPARTITE ENTANGLED SYSTEMS

2003 ◽  
Vol 17 (30) ◽  
pp. 5737-5747 ◽  
Author(s):  
HONG-YI FAN ◽  
NIAN-QUAN JIANG
Keyword(s):  
Distribution Function ◽  
Wigner Function ◽  
Physical Meaning ◽  
Wigner Distribution ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Wigner Distribution Function ◽  
Wigner Operator ◽  
Tripartite Entangled State

Based on the observation that for an entangled-particles system, the physical meaning of the Wigner distribution function should lie in that its marginal distributions would give the probability of finding the particles in an entangled way, we establish a tomography theory for the Wigner function of tripartite entangled systems. The newly constructed tripartite entangled state representation of the three-mode Wigner operator plays a central role in realizing this goal.

TIME EVOLUTION OF THE NONCLASSICALITY FOR THE FOCK STATES AND THEIR SUPERPOSITION STATES BY THE WIGNER FUNCTION

2011 ◽  
Vol 25 (16) ◽  
pp. 1401-1415 ◽  
Author(s):  
KUN SI ◽  
NING-LI ZHU ◽  
HUAN-YU JIA
Keyword(s):  
Time Evolution ◽  
Wigner Function ◽  
Gain Coefficient ◽  
Wigner Functions ◽  
Fock States ◽  
Negative Region ◽  
Cavity Radiation ◽  
Superposition States

The Wigner functions of the Fock states and their superposition states have negative value clearly. We focus on discussing the time evolution of the Fock states and their superposition states by the Wigner function under the coherent drive (pumping laser) and dissipation channels (cavity radiation). The results show that the negative region of their Wigner function gradually diminishes as the time kt or the gain coefficient g increasing. In addition, the disappearing time is related to the value of g - k. The loss of non-classical features becomes slower when g increases with the k > g; there is the "frozen zone" when k = g; then the loss of non-classical features becomes faster when g increases with k < g.

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