An exactly solvable model for metal-insulator phase transition

A simple model of electrons interacting with photons which displays a metal-insulator phase transition in the case of s.c. and b.c.c. tight-binding bands is studied. A proof is given that the model is exactly solvable in the thermodynamic limit.     

Minimal Brownian ratchet: an exactly solvable model

We develop an analytically solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations, we obtain the steady-state probabilities. Generally, the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space, we find the null curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force.     

Heat flow in an exactly solvable model

A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures. The stationary measures are obtained when the chain is finite; the thermodynamic limit is then considered, approach to the Gibbs distribution is proven, and a linear temperature profile is obtained.     

Feynman's ratchet and pawl: an exactly solvable model

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear-response theory.     

Correlation functions in an exactly solvable tefface-ledge-kink model

We solve exactly a terrace-ledge-kink (TLK) model describing a vicinal section of a crystal surface at a microscopic level, with either repulsive or attractive interactions between the ledges. As expected there is a faceting, or reconstructive, phase transition, driven either by temperature or by the chemical potential, that controls the mean slope of the surface. In the rough phase we carry out a thorough investigation of microscopic thermal fluctuations of the interface. This is done by combining Bethe ansatz and Conformal Field Theory methods in order to calculate appropriately defined correlators.     

Unexpected scenario of glass transition in polymer globules: an exactly enumerable model

We introduce a lattice model of glass transition in polymer globules. This model exhibits ergodicity breaking in which the disjoint regions of phase space do not arise uniformly, but as small chambers whose number increases exponentially with polymer density. Chamber sizes obey power law distribution, making phase space similar to a fractal foam. This clearly demonstrates the importance of the phase space geometry and topology in describing any glass-forming system, such as semicompact polymers during protein folding.     

The reduced α-amplitude in an exactly solvable model

In recent work by Fliessbach the removal of an α-particle from a nucleus under the influence of a perturbation was considered. Using certain approximations the many-body transition matrix element was reduced to a one-body matrix element. This one-body matrix element showed that the appropriate bound α-amplitude in the initial nucleus (reduced amplitude) depends on the energy transferred to the removed α-particle. The present paper deals with an analytic model in which the one-body transition matrix element as given in that work can be derived exactly from the original microscopic matrix element.     

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Fröhlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Fröhlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.     

An exactly solvable model for two-dimensional non-Hermitian quasicrystals

The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson localization has been extended to many fields of physics,including the quasiperiodic or incommensurate systems.     

An exactly solvable infinite-ranged model for sliding charge-density-waves

An infinite-ranged model for the sliding charge-density-wave (CDW) with periodic harmonic impurity potentials is shown to be solvable exactly in a whole range of the electric field strength. The solution yields some distinct features of the sliding CDW which were not reported in the same infinite-ranged model but with a sinusoidal impurity potential. The results on the nonlinear conductivity are discussed in comparison with the experiments on NbSe₃.     

Exciton dephasing in quantum dots due to LO-phonon coupling: an exactly solvable model

It is widely believed that, due to its discrete nature, excitonic states in a quantum dot coupled to dispersionless longitudinal-optical (LO) phonons form everlasting mixed states (exciton polarons) showing no line broadening in the spectrum. This is indeed true if the model is restricted to a limited number of excitonic states in a quantum dot. We show, however, that extending the model to a large number of states results in LO phonon-induced spectral broadening and complete decoherence of the optical response.     

An exactly solvable model for two-dimensional non-Hermitian quasicrystals

Ultrasound focusing in three-dimensional(3 D)space is of crucial and enduring significance in a variety of biomedical and industrial applications.Conventional ultrasound focusing based on active phase array or passive geometry of bulky size is unable to realize the 3 D arbitrary focusing with subwavelength resolution.Acoustic metamaterial of complex deep-subwavelength microstructure has facilitated the advanced airborne-sound-focusing but is inevitably not applicable for underwater ultrasound,restricted by the law between the multi-modes coupling/thermal viscosity and the feature size of the structure.Here,we aim to circumvent the restriction by increasing the feature size of the metamaterial while keeping the compact overall geometry,and realize the robust subwavelength ultrasound focusing with the sparse metalens of the wavelength-scale meta-atom.We theoretically propose and demonstrate numerically and experimentally the broadband arbitrary ultrasound focusing in 3 D space.The axial and off-axis ultrasound focusing with the subwavelength resolution(FWHM<0.58λ)are achieved by the spatially sparse and compact metalens within one-octave bandwidth.With advantages of 3 D freewheeling focusing,subwavelength resolution,spatial sparsity,geometric simplicity,and broadband,the sparse metalens would offer more initiatives to advanced researches in ultrasound focusing and empower applications such as precise biomedical imaging and therapy,nondestructive evaluation,integrated and multiplexed ultrasound devices.     

Distribution of pore-size in an exactly solvable two-dimensional biomembrane model

A model for a two-dimensional lipid bilayer in which both short range repulsive forces and long range attractive forces play a role, and which can be solved exactly, is discussed. It is shown that the bilayer consists of long stretches of relatively densely packed lipids separated by small pores. The statistical distributions of number and size of the pores are calculated from first principles.     

Topological order in an exactly solvable 3D spin model

We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R²) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.     

Static polarizability of an exactly solvable model of diatomic molecule

Summary A very simple one-dimensional model for a one-electron diatomic molecule, under the influence of a weak static electric field, is investigated by perturbation theory. The dipole polarizabilities for the two only bound states supported by this molecular model are evaluated as a function of the internuclear distance.

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Riassunto Si studia perturbativamente l'influenza di un debole campo elettrico statico su un modello monodimensionale semplificato di molecola biatomica contenente un unico elettrone “attivo”. Si calcola la polarizzabilità di dipolo nei due soli stati legati supportati dal modello in questione, mettendo in evidenza la dipendenza dalla distanza internucleare.

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Резюме В рамках теории возмущений исследуется влияние слабого статического злектрического поля на улрощенную одномерную модель двухатомной молекулы с одним “активным” злектроном. Вычисляется дилольная поляризуемость для двух связанных состояний, долускаемых рассматриваемой моделью молекулы, как функция расстояния между ядрами.

     

Fractional statistics in one dimension: view from an exactly solvable model

One-dimensional fractional statistics is studied using the Calogero-Sutherland model (CSM) which describes a system of non-relativistic quantum particles interacting with an inverse-square two-body potential on a ring. The inverse-square exchange can be regarded as a pure statistical interaction and this system can be mapped to an ideal gas obeying the fractional exclusion and exchange statistics. The details of the exact calculations of the dynamical correlation functions or this ideal system is presented in this paper. An effective low-energy one-dimensional “anyon” model is constructed; and its correlation functions are found to be in agreement with those in the CSM; and this agreement provides an evidence for the equivalence of the first- and the second-quantized construction of the 1D anyon model at least in the long-wavelength limit. Furthermore, the finite-size scaling applicable to the conformally invariant systems is used to obtain the complete set of correlation exponents for the CSM.