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.     

Interpretation of an exactly solvable two-component plasma

The interpretation of the exact calculation of the partition function and correlations of a two-component plasma obtained earlier is considered. The system has species of charge ratio 12 which are constrained to lie on a circle and interact via the two-dimensional Coulomb potential. By studying the exact results we gain an understanding of why the excess thermodynamic quantities of the two component system can be well approximated by the sum of the appropriate excess thermodynamic quantities of the one-component systems.     

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.     

Twist in an exactly solvable directed lattice ribbon

We investigate the transition between a twisted regime and a disordered regime in a directed ribbon model on a cubic lattice. A fugacity corresponding to an interaction which models half-twists in the ribbon is introduced and the interacting model is solved exactly. Our results suggest that conformational entropy and a local interaction which induces twist are key ingredients to model qualitatively the crossover behavior between a twisted (helical) regime and a denatured regime in duplex biopolymers such as DNA.     

Single-particle properties in an exactly solvable A-body system

A recent theorem states that for quantum many-body systems with short-range interactions the following property holds: the single-particle overlap functions, spectroscopic factors and separation energies of bound eigenstates of the (A ? 1)-particle system are fully determined by the one-body density matrix of the A-particle system in its ground state. We confirm this property, by explicit construction, for the case of a schematic, exactly solvable system.     

New class of exactly solvable one-dimensional disordered electron hopping systems

Two types of disordered chains are presented, which allow for the exact calculation of the (configurational averaged) density of states in terms of a continued fraction. The first model contains a certain type of site-diagonal disorder and is a generalization of Lloyd's model; it refers to a substitutional alloy.The second model contains site-off-diagonal (hopping) disorder and may refer to a generalized alloy—analog treatment of a Hubbard chain.     

Time-dependent exactly solvable models for quantum computing

A time-dependent periodic Hamiltonian admitting exact solutions is applied to construct a set of universal gates for a quantum computer. The time evolution matrices are obtained in an explicit form and used to construct logic gates for computation. A way of obtaining an entanglement operator is discussed, too. The method is based on transformation of soluble time-independent equations into time-dependent ones by employing a set of special time-dependent transformation operators. The text was submitted by the authors in English.     

Continuum spin system as an exactly solvable dynamical system

The continuum limit of a one-dimensional classical spins with nearest neighbour Heisenberg interaction is shown to be an exactly solvable system and that its dynamics describable by the nonlinear Schrödinger equation. N-soliton solutions for the energy density exist.     

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 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.     

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.     

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.