Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component ϕ4\phi^4 theory

Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.Comment: 16pages, Latex, typographical errors are correcte

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures

Results of numerical simulations of a recently derived most general dissipative-dispersive PDE describing evolution of a film flowing down an inclined plane are presented. They indicate that a novel complex type of spatiotemporal patterns can exist for strange attractors of nonequilibrium systems. It is suggested that real-life experiments satisfying the validity conditions of the theory are possible: the required sufficiently viscous liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations available upon or reques

Causal amplitudes in the Schwinger model at finite temperature

We show, in the imaginary time formalism, that the temperature dependent parts of all the retarded (advanced) amplitudes vanish in the Schwinger model. We trace this behavior to the CPT invariance of the theory and give a physical interpretation of this result in terms of forward scattering amplitudes of on-shell thermal particles.Comment: 4 pages with 5 figures, two minor typos corrected, to appear in Physical Review

On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible $Z_n$ meromorphic orbifold constructions of ${\cal V}^\natural$ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group $M$ together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give ${\cal V}^\natural$ itself or the Leech theory. This constraint on the meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $\Delta F_L := \ln (P_{L, max} / P_{L, min}) \propto L^\theta$ should be observed, where $\theta>0$ is the "violation of hyperscaling" exponent. Since $\theta$ is substantially non-zero, the scaling of $\Delta F_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $\Delta F_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.Comment: sent to J. Phys. Cond. Mat

Electron properties of carbon nanotubes in a periodic potential

A periodic potential applied to a nanotube is shown to lock electrons into incompressible states that can form a devil's staircase. Electron interactions result in spectral gaps when the electron density (relative to a half-filled Carbon pi-band) is a rational number per potential period, in contrast to the single-particle case where only the integer-density gaps are allowed. When electrons are weakly bound to the potential, incompressible states arise due to Bragg diffraction in the Luttinger liquid. Charge gaps are enhanced due to quantum fluctuations, whereas neutral excitations are governed by an effective SU(4)~O(6) Gross-Neveu Lagrangian. In the opposite limit of the tightly bound electrons, effects of exchange are unimportant, and the system behaves as a single fermion mode that represents a Wigner crystal pinned by the external potential, with the gaps dominated by the Coulomb repulsion. The phase diagram is drawn using the effective spinless Dirac Hamiltonian derived in this limit. Incompressible states can be detected in the adiabatic transport setup realized by a slowly moving potential wave, with electron interactions providing the possibility of pumping of a fraction of an electron per cycle (equivalently, in pumping at a fraction of the base frequency).Comment: 21 pgs, 8 fig

Formation of the internal structure of solids under severe action

On the example of a particular problem, the theory of vacancies, a new form of kinetic equations symmetrically incorporation the internal and free energies has been derived. The dynamical nature of irreversible phenomena at formation and motion of defects (dislocations) has been analyzed by a computer experiment. The obtained particular results are extended into a thermodynamic identity involving the law of conservation of energy at interaction with an environment (the 1st law of thermodynamics) and the law of energy transformation into internal degree of freedom (relaxation). The identity is compared with the analogous Jarzynski identity. The approach is illustrated by simulation of processes during severe plastic deformation, the Rybin kinetic equation for this case has been derived.Comment: 9 pages, 5 figure

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $\phi$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $\phi=0.60$ for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including new dat