P Buonsante and V Penna 2008 J. Phys. A: Math. Theor. 41 175301 doi:10.1088/1751-8113/41/17/175301
Some remarks on the coherent-state variational approach to nonlinear boson models
P Buonsante and V Penna
Show affiliationsMean-field pictures based on the standard time-dependent variational approach have widely been used in studying nonlinear many-boson systems such as the Bose–Hubbard model. Mean-field schemes relevant to Gutzwiller-like trial states |F
, number-preserving states |ξ and Glauber-like trial states |Z are compared to evidence of specific properties of such schemes. After deriving the Hamiltonian picture relevant to |Z from that based on |F, the latter is shown exhibiting a Poisson algebra equipped with a Weyl–Heisenberg subalgebra which preludes to the |Z-based picture. Then states |Z are shown to be a superposition of 
-boson states |ξ, and the similarities/differences between the |Z-based and |ξ-based pictures are discussed. Finally, after proving that the simple, symmetric state |ξ indeed corresponds to a SU(M) coherent state, a dual version of states |Z and |ξ in terms of momentum-mode operators is discussed together with some applications.
- PACS
- MSC
-
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
- Subjects
-
Quantum gases, liquids and solids
- Dates
-
Issue 17 (2 May 2008)
Received 23 November 2007, in final form 12 March 2008
Published 15 April 2008
-
Some remarks on the coherent-state variational approach to nonlinear boson models
P Buonsante and V Penna 2008 J. Phys. A: Math. Theor. 41 175301
-
Spin Relaxation of Electrons in Single InAs Quantum Dots
Ma Shan-Shan et al 2009 Chinese Phys. Lett. 26 117201
-
A Sensitive Scheme to Observe Weak Photo-Refraction Effects in Some Nonlinear Optical Crystals Pumped by Ultrashort Optical Pulses
Xu Shi-Xiang et al 2009 Chinese Phys. Lett. 26 114209
-
Quaternionic soliton equations from Hamiltonian curve flows in
Stephen C Anco and Esmaeel Asadi 2009 J. Phys. A: Math. Theor. 42 485201
-
Properties of a class of block-iterative methods
Tommy Elfving and Touraj Nikazad 2009 Inverse Problems 25 115011
-
The semiclassical origin of curvature effects in universal spectral statistics
Daniel Waltner et al 2009 J. Phys. A: Math. Theor. 42 292001
-
Clusters of solutions and replica symmetry breaking in random k-satisfiability
Andrea Montanari et al J. Stat. Mech. (2008) P04004
-
Photo-induced formation and self-assembling of gold nanoparticles in aqueous solution of amphiphilic dendrimers with oligo(p-phenylene vinylene) core branches and oligo(ethylene oxide) terminal chains
Dong Wook Chang and Liming Dai 2007 Nanotechnology 18 365605
-
Effect of K3PO4 addition as sintering inhibitor during calcination of Y2O3 nanoparticles
K Soga et al 2009 J. Phys.: Conf. Ser. 191 012003
-
Reply to the comment on 'New geometry for the quasi-binary incident electron–centre of mass collision in the (e, 3e) process on He'
Rakesh Choubisa and K K Sud 2008 J. Phys. B: At. Mol. Opt. Phys. 41 208002
Users also read
What's this?-
Discrete
-symmetric models of scattering
- Conductivity of dielectric and thermal atom–wall interaction
- Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain