The Vlasov equation and the Hamiltonian mean-field model

We show that the quasi-stationary states of homogeneous (zero magnetization) states observed in the N-particle dynamics of the Hamiltonian mean-field (HMF) model are nothing but Vlasov stable homogeneous states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis q-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite N effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann–Gibbs equilibrium.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms are calculated for relative energies below the excitation threshold for the N₂ (j=2) rotational state. The close coupling method is used and the coupled differential equations are solved numerically. Very sharp resonances (corresponding to a lifetime of 10^?10 sec) caused by quasistable states of the N₂He system are found in the calculated cross section, when the closed channels corresponding to the N₂ (j=2) states were included in the coupled equations. The position of the resonances is compared with the calculated energy eigenvalues of the corresponding two body potential. Furthermore the equilibrium concentration of the N₂He quasistable and orbiting states is calculated at 80 °K andp _{N 2}=1 Atm. Both concentrations are found to be 1%.     

General linear response formula for non integrable systems obeying the Vlasov equation

Long-range interacting N-particle systems get trapped into long-living out-of-equilibrium stationary states called quasi-stationary states (QSS). We study here the response to a small external perturbation when such systems are settled into a QSS. In the N → ∞ limit the system is described by the Vlasov equation and QSS are mapped into stable stationary solutions of such equation. We consider this problem in the context of a model that has recently attracted considerable attention, the Hamiltonian mean field (HMF) model. For such a model, stationary inhomogeneous and homogeneous states determine an integrable dynamics in the mean-field effective potential and an action-angle transformation allows one to derive an exact linear response formula. However, such a result would be of limited interest if restricted to the integrable case. In this paper, we show how to derive a general linear response formula which does not use integrability as a requirement. The presence of conservation laws (mass, energy, momentum, etc.) and of further Casimir invariants can be imposed a posteriori. We perform an analysis of the infinite time asymptotics of the response formula for a specific observable, the magnetization in the HMF model, as a result of the application of an external magnetic field, for two stationary stable distributions: the Boltzmann-Gibbs equilibrium distribution and the Fermi-Dirac one. When compared with numerical simulations the predictions of the theory are very good away from the transition energy from inhomogeneous to homogeneous states.     

Size effect on magnetic properties of a nano-graphene bilayer structure: A Monte Carlo study

In this paper we use the Monte Carlo simulations to investigate the magnetic properties of an Ising ferromagnetic–antiferromagnetic model. The system is based on a nano-graphene structure-like bilayer with two bloc sizes: N=24 and 42 spins. For each size N, the upper layer A is formed with spin −3/2, whereas the lower layer B is composed of spin −5/2. We only consider the first nearest-neighbor interactions between the sites i and j. The magnetic properties are studied, in the absence as well as in the presence of a crystal magnetic field, and an external magnetic field. The increasing temperature and crystal field as well as the inter-layer coupling constant, are also studied for this system sizes N=24 and 42 spins. The zero-field-cooled and the field cooled magnetization behaviors are investigated for different values of external magnetic field and a fixed value of exchange interaction between the two blocs. The magnetizations as well as the magnetic susceptibilities versus the temperature are used in order to obtain blocking temperature.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

Organic high-spin systems: synthesis, electrochemical and ETSF studies of a series of tetraaryl-meta-phenylenediamines

A series of N,N,N′,N′-tetraaryl-1,3-phenylenediamines with various substituents at the para-position of peripheral rings were designed and synthesized. Electrochemical and novel electron transfer stopped-flow methods were invoked for characterizing the absorption spectra of the corresponding short-lived mono- and dicationic states. Both thermodynamic and kinetic stabilization are required to extend the lifetime of the dicationic states. Useful molecular design rules for stabilizing the dicationic states of N,N,N′,N′-tetraaryl-1,3-phenylenediamines as precursors for positively charged high-spin systems were elucidated.     

Novel multi-band quantum soliton states for a derivative nonlinear Schrödinger model

We show that localized N-body soliton states exist for a quantum integrable derivative nonlinear Schrödinger model for several nonoverlapping ranges (called bands) of the coupling constant η. The number of such distinct bands is given by Euler's φ-function which appears in the context of number theory. The ranges of η within each band can also be determined completely using concepts from number theory such as Farey sequences and continued fractions. We observe that N-body soliton states appearing within each band can have both positive and negative momentum. Moreover, for all bands lying in the region η>0, soliton states with positive momentum have positive binding energy (called bound states), while the states with negative momentum have negative binding energy (anti-bound states).     

Coherence transition of small Josephson junctions coupled to a single-mode resonant cavity: Connection to the Dicke model

We calculate the thermodynamic properties of a collection of N small Josephson junctions coupled to a single-mode resonant electromagnetic cavity, at finite temperature T, using several approaches. In the first approach, we include all the quantum-mechanical levels of the junction, but treat the junction-cavity interaction using a mean-field approximation developed previously for $T=0$. In the other approaches, the junctions are treated including only the two lowest energy levels per junction, but with two different Hamiltonians. The first of these maps onto the Dicke model of quantum optics. The second is a modified Dicke model which contains an additional XY-like coupling between the junctions. The modified Dicke model can be treated using a mean-field theory, which in the limit of zero XY coupling gives the solution of the Dicke model in the thermodynamic limit using Glauber coherent states to represent the cavity. In all cases, for an N-independent junction-cavity coupling, there is a critical junction number N above which there is a continuous transition from incoherence to coherence with decreasing T. If the coupling scales with N so as to give a well-behaved thermodynamic limit, there is a critical minimum coupling strength for the onset of coherence. In all three models, the cavity photon occupation numbers have a non-Bose distribution when the system is coherent.     

Lebensdauermessungen in N14

The Doppler Shift Attenuation Method was used to measure the lifetimes of the four lowest negative parity states in N¹⁴. The states were produced in the reaction C¹²(He³,p)N¹⁴ and were found to have mean lifetimes State (MeV) lifetime (ps) 4.91τ<0.050 5.10 4.5<τ<20 5.69τ≦0.036 5.83τ>4.5 The results obtained are compared with the predictions of the nuclear shell model.     

Application of point-group bases to f−fd transitions of lanthanide and actinide ions doped in crystals

The application of point-group coupling coefficients to the modeling of f^N↔f^N−1d transitions is discussed. There are several possible coupling schemes for the states of the f^N−1d configuration. Formulae for matrix elements of the Hamiltonian for the f^N−1d configuration and the relative line strengths for f^N↔f^N−1d transitions are derived. As an example, the f-d absorption spectrum of the crystal Yb²⁺: SrCl₂ is calculated using coupling coefficients based on the software developed by Butler and co-workers, which makes use of the Racah-Wigner calculus. The advantages and disadvantages of various coupling schemes are demonstrated. These coupling schemes are related to the simple model for f-d transitions.     

Variational approach for the N-state spin and gauge Potts model

A hamiltonian variational treatment is applied both to the spin Potts model and to its gauge version for any number of states N and spatial dimensions d?2. Regarding the former we reproduce the correct critical coupling and latent heat for not too low N and d. For the latter, our approach turns the gauge theory into an equivalent d-dimensional classical spin model, which evaluated for d + 1 = 4 gives results in agreement with 1/N expansions.     

Chaoticity and intruder states for 147Gd and 115In

The number variance is calculated for the energy spectra of ¹⁴⁷Gd and ¹¹In, which have been previously calculated in a particle-core coupling model, eventually including the intruder states (1 particle-1 hole excitations across the major closed shell at N=82 or Z=50, respectively). The inclusion of intruder states leads to an increase of the degree of chaoticity.     

Strong coupling polaron theory and translational invariance

We develop a systematic, manifestly translation invariant, strong coupling theory for nonrelativistic Hamiltonians of the polaron type. As in earlier strong coupling theories, the position of the polarization well is a collective coordinate. The field is expanded in a set of basis functions centered about the well with three amplitudes deleted. A particle coordinate relative to the polarization center is introduced. The new coordinates are introduced using a point canonical transform leading to a Hermitian Hamiltonian, with properly normalized wavefunctions, and with a Jacobian that is evaluated in closed form. All subsequent approximations to the states are manifestly translation invariant. For the ground state the energy of the recoil terms to leading order depend on the coupling constant g as g^?4. The intrinsic part of the Hamiltonian determines the energy terms of order g⁴ and g⁰. An adiabatic canonical transformation is used to calculate all terms through order g^?4. The coefficients depend on the Green's function for the electron in a static potential well. We determine the first three terms in the inverse coupling constant expansion of the effective mass.     

Time evolution of a quantum mechanical maser model

The time evolution of the Dicke maser model describing N spins ($\text{s =}\text{1}\text{2}$) interacting by a dipole coupling with one mode of an electromagnetic field, is studied for finite N. The mean photon number and its mean square deviation can be calculated as functions of time for various initial states. For not too large times, these quantities show a periodic behavior given by elliptic functions.     

扩展哈伯德模型中原子团簇的结构和热力学性质研究

采用数值精确对角化方法,在加入了近邻电子库仑排斥作用的扩展哈伯德模型中对原子数N=5和N=6的原子团簇进行了研究.首先得到了对应于不同强度的电子在位库仑作用能U、近邻排斥作用能V,以及不同电子填充数的团簇的优化结构和相应的总自旋S.研究结果表明,电子的近邻排斥能V的引入会使团簇向成键数目减少的链状或星状结构改变.然后结合团簇的能级特征,分析了团簇的热容和磁化率等热力学特性,其中热容曲线的峰值位置可由团簇的低能激发给出合理的解释.     

The construction of the eigenstates for nonlinear Schrödinger model with supermatrices and attractive coupling

A quantum nonlinear Schrödinger model with supermatrices and attractive coupling is studied by using the quantum inverse scattering method. The eigenstates of the Hamiltonian and the infinite number of the conserved quantities of the system are constructed. In particular, theN-particle bound states with the mixture of bosons and fermions are found. The energy of theN-particle eigenstate are Σ _i=1 ^N andNp ² ?N(N ²?1)c ²/12 for the scattering state and the bound state respectively.     

Singularrenormalization group transformations and first order phase transitions (I)

It is argued that standard position and momentum space renormalization group (RG) transformations are singular (i.e. lead to a singular hamiltonian after a finite number of RG steps) in large regions of the coupling constant space. It is shown in the d = 3, φ⁶ O(N)_N→∞ model that the momentum space RG transformation is singular in all those points of the coupling constant space, where metastable states exist. This region includes the full first order phase transition surface and its neighbourhood. Several other examples are discussed to illustrate that this phenomenon is generic and not a specific large N effect. Some earlier and recent anomalous Monte Carlo renormalization group results are consistent with this conclusion.     

Directed transport of modulated structures in the Frenkel–Kontorova model with a pulsating coupling

We study the directed transport of commensurate and incommensurate modulated phases of the Frenkel–Kontorova model by (parametric driving) periodic pulsed variation of the nearest-neighbor coupling in the dissipative limit of the dynamics. We obtain that a directed current flow appears as the amplitude of the pulsating coupling C increases above a threshold coupling C_th. This threshold coupling depends on the average interspacing ω between the oscillators displaying singularities as the system becomes commensurable with the underlying lattice. By making use of the discommensuration theory of modulated phases we obtain that the dependence of the directed current on ω is a piecewise linear function with integer slope. Numerical results confirm these predictions.