Research on mesoscopic inductance–capacitance coupling circuit employing an unitary operator and the IWOP technique

2015 ◽  
Vol 29 (17) ◽  
pp. 1550084
Author(s):  
Xiu-Xia Wang
Keyword(s):  
Ground State ◽  
Uncertainty Relation ◽  
Unitary Operator ◽  
Quantum Fluctuations ◽  
Quantum Effects ◽  
Iwop Technique ◽  
Squeezed State ◽  
Coupling Term ◽  
Coupling Circuit ◽  
Capacitance Coupling

Employing a special unitary operator and the virtue of the technique of integration within an ordered product (IWOP), we research on the quantum effects for an inductance–capacitance coupling double L–C circuit. It is found that it is convenient to research on the mesoscopic circuit with such an operator. First, eliminating the coupling term of Hamiltonian becomes easier than other methods. Second, the system’s ground state can be easily generalized into a two-mode squeezed state. Thus, the quantum fluctuations of the circuit and the variances of current in each loop are calculated, the charge-current uncertainty relation is revealed. As a result, both the uncertainty relation and fluctuation of the current in each loop become larger when [Formula: see text] is larger or [Formula: see text] is smaller.

Loss of classicality in the alternating spin-½/spin-1 chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions

2022 ◽  
Author(s):  
Abhiroop Lahiri ◽  
Swapan K Pati
Keyword(s):  
Ground State ◽  
Nearest Neighbor ◽  
Spiral Structure ◽  
Exchange Interactions ◽  
Quantum Fluctuations ◽  
Wave Theory ◽  
Range Order ◽  
Density Matrix Renormalization Group ◽  
Density Matrix Renormalization ◽  
Spin Spiral

Abstract We have considered and alternating spin-½/spin-1 chain with nearest-neighbor (J1), next-nearest neighbor (J2) antiferromagnetic Heisenberg interactions along with z-component of the Dzyaloshinskii-Moriya(DM) (Dz) interaction. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J2 introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J1 along with Dzintroduces a short range order but develops long range order along the XY plane. J1 along with J2induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the Dz term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.

EFFECT OF ASYMMETRY IN A BISTABLE SYSTEM WITH QUANTUM FLUCTUATIONS: STRONG FRICTION LIMIT

2011 ◽  
Vol 25 (32) ◽  
pp. 4331-4338
Author(s):  
CHUNHUA ZENG ◽  
AILING GONG ◽  
YUHUI LUO
Keyword(s):  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Quantum Fluctuations ◽  
Quantum Effects ◽  
Passage Time ◽  
Bistable System ◽  
Original Position ◽  
Classical Counterpart ◽  
The Mean ◽  
Resonant Activation

In this paper, we study the effect of asymmetry of the potential in a bistable system with quantum fluctuations. Within the quantum Smoluchowski regime, the expressions for the mean first passage time (MFPT) and signal-to-noise ratio (SNR) of the system are obtained, respectively. Based on the MFPT and SNR, we consider both, the overdamped quantum case and its classical counterpart, the effects of the quantum fluctuations and the asymmetry of the potential on the MFPT and SNR are discussed. Our main results show that (i) the quantum fluctuations facilitate the particle to reach the destination from its original position, (ii) the resonant activation (RA) phenomena can be observed with varying asymmetry of the potential, and (iii) the quantum effects in an asymmetric bistable system about SNR are prominent for lower temperatures and smaller asymmetry of the potential. Moreover, the quantum effects enhance the stochastic resonance (SR) of the system.

POSITIVE GROUND STATES FOR A CLASS OF SUPERLINEAR -LAPLACIAN COUPLED SYSTEMS INVOLVING SCHRÖDINGER EQUATIONS

2019 ◽  
Vol 109 (2) ◽  
pp. 193-216 ◽  
Author(s):  
J. C. DE ALBUQUERQUE ◽  
JOÃO MARCOS DO Ó ◽  
EDCARLOS D. SILVA
Keyword(s):  
Large Class ◽  
Ground State ◽  
Variational Approach ◽  
Ground States ◽  
Nehari Manifold ◽  
Coupled Systems ◽  
Coupling Term ◽  
Ground State Solutions ◽  
Image Position ◽  
The Nehari Manifold

We study the existence of positive ground state solutions for the following class of $(p,q)$-Laplacian coupled systems $$\begin{eqnarray}\left\{\begin{array}{@{}lr@{}}-\unicode[STIX]{x1D6E5}_{p}u+a(x)|u|^{p-2}u=f(u)+\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D706}(x)|u|^{\unicode[STIX]{x1D6FC}-2}u|v|^{\unicode[STIX]{x1D6FD}}, & x\in \mathbb{R}^{N},\\ -\unicode[STIX]{x1D6E5}_{q}v+b(x)|v|^{q-2}v=g(v)+\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D706}(x)|v|^{\unicode[STIX]{x1D6FD}-2}v|u|^{\unicode[STIX]{x1D6FC}}, & x\in \mathbb{R}^{N},\end{array}\right.\end{eqnarray}$$ where $1<p\leq q<N$. Here the coefficient $\unicode[STIX]{x1D706}(x)$ of the coupling term is related to the potentials by the condition $|\unicode[STIX]{x1D706}(x)|\leq \unicode[STIX]{x1D6FF}a(x)^{\unicode[STIX]{x1D6FC}/p}b(x)^{\unicode[STIX]{x1D6FD}/q}$, where $\unicode[STIX]{x1D6FF}\in (0,1)$ and $\unicode[STIX]{x1D6FC}/p+\unicode[STIX]{x1D6FD}/q=1$. Using a variational approach based on minimization over the Nehari manifold, we establish the existence of positive ground state solutions for a large class of nonlinear terms and potentials.

Influence of quantum fluctuations on the ground state of quasi-one-dimensional triangular antiferromagnet

2000 ◽  
Vol 284-288 ◽  
pp. 1623-1624
Author(s):  
B.S. Dumesh ◽  
V.A. Panfilov ◽  
A.M. Tikhonov ◽  
D.N. Fourzikov
Keyword(s):  
Ground State ◽  
Quantum Fluctuations ◽  
One Dimensional

ON THE REPRESENTATION OF THE WIGNER ALGEBRA AND WIGNER DEFORMATION OF THE FERMION ALGEBRA

2013 ◽  
Vol 28 (17) ◽  
pp. 1350074 ◽  
Author(s):  
WON SANG CHUNG
Keyword(s):  
Coherent State ◽  
Ground State ◽  
Uncertainty Relation ◽  
Finite Dimension ◽  
Fock Space ◽  
Fermion Algebra

In this paper, we investigate the representation of the Wigner algebra by using the q-calculus like approach. For this algebra, the coherent state is constructed and the uncertainty relation for the ground state is discussed. Following Wigner's approach, the Wigner deformation of the fermion algebra is obtained and its Fock space is shown to have finite dimension.

UNCERTAINTY RELATIONS FOR THE TIME-DEPENDENT SINGULAR OSCILLATOR

2006 ◽  
Vol 20 (10) ◽  
pp. 1211-1231 ◽  
Author(s):  
J. R. CHOI ◽  
I. H. NAHM
Keyword(s):  
Harmonic Oscillator ◽  
Excited States ◽  
Ground State ◽  
Coherent States ◽  
System Approach ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Number State ◽  
State Uncertainty

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

Sign in / Sign up

Export Citation Format

Share Document