arXiv subjects

Gerhard Müller

Publications and source records attributed to Gerhard Müller.

33 records · Page 2Linked to original sources

arXiv2015

Monodisperse hard rods in external potentials

We consider linear arrays of cells of volume $V_\mathrm{c}$ populated by monodisperse rods of size $σV_\mathrm{c}$, $σ=1,2,\ldots$, subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as $V_\mathrm{c}\to0$, $σ\to\infty$ at nonzero and finite $σV_\mathrm{c}$, connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.

cond-mat.stat-mech↗

arXiv2015

Coil-helix transition of polypeptide at water-lipid interface

We present the exact solution of a microscopic statistical mechanical model for the transformation of a long polypeptide between an unstructured coil conformation and an $α$-helix conformation. The polypeptide is assumed to be adsorbed to the interface between a polar and a non-polar environment such as realized by water and the lipid bilayer of a membrane. The interfacial coil-helix transformation is the first stage in the folding process of helical membrane proteins. Depending on the values of model parameters, the conformation changes as a crossover, a discontinuous transition, or a continuous transition with helicity in the role of order parameter. Our model is constructed as a system of statistically interacting quasiparticles that are activated from the helix pseudo-vacuum. The particles represent links between adjacent residues in coil conformation that form a self-avoiding random walk in two dimensions. Explicit results are presented for helicity, entropy, heat capacity, and the average numbers and sizes of both coil and helix segments.

cond-mat.soft↗

arXiv2014

Disks in a narrow channel jammed by gravity and centrifuge: profiles of pressure, mass density and entropy density

This work investigates jammed granular matter under conditions that produce heterogeneous mass distributions on a mesoscopic scale. We consider a system of identical disks that are confined to a narrow channel, open at one end and closed off at the other end. The disks are jammed by the local pressure in a gravitational field or centrifuge. All surfaces are hard and frictionless. We calculate the profiles of pressure, mass density, and entropy density on a mesoscopic length scale under the assumption that the jammed states are produced by random agitations of uniform intensity along the channel. These profiles exhibit trends and features governed by the balancing of position-dependent forces and potential energies. The analysis employs a method of configurational statistics that uses interlinking two-disk tiles as the fundamental degrees of freedom. Configurational statistics weighs the probabilities of tiles according to competing potential energies associated with gravity and centrifugation. Amendments account for the effects of the marginal stability of some tiles due to competing forces.

cond-mat.stat-mech↗

arXiv2013

Interacting hard rods on a lattice: Distribution of microstates and density functionals

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.

cond-mat.stat-mech↗

arXiv2012

Interlinking motifs and entropy landscapes of statistically interacting particles

The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor coupling is used to construct a system of floating particles characterized by motifs of up to six consecutive local spins. The spin couplings cause the assembly of particles which, in turn, remain free of interaction energies even at high density. All microstates are configurations of particles from one of three different sets, excited from pseudo-vacua associated with ground states of periodicities one, two, and four. The motifs of particles and elements of pseudo-vacuum interlink in two shared site variables. The statistical interaction between particles is encoded in a generalized Pauli principle, describing how the placement of one particle modifies the options for placing further particles. In the statistical mechanical analysis arbitrary energies can be assigned to all particle species. The entropy is a function of the particle populations. The statistical interaction specifications are transparently built into that expression. The energies and structures of the particles alone govern the ordering at low temperature. Under special circumstances the particles can be replaced by more fundamental particles with shorter motifs that interlink in only one shared site variable. Structures emerge from interactions on two levels: particles with shapes from coupled spins and long-range ordering tendencies from statistically interacting particles with shapes.

cond-mat.stat-mech↗

arXiv2005

Dimer and trimer fluctuations in the s=1/2 transverse XX chain

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional s=1/2 XX model in a transverse magnetic field ($\parallel z$) are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations whereas that of the trimer fluctuation operator involves two-fermion and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared with corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.

cond-mat.stat-mech↗

arXiv1997

Exact two-spin dynamic structure factor of the one-dimensional s=1/2 Heisenberg-Ising antiferromagnet

The exact 2-spinon part of the dynamic spin structure factor $S_{xx}(Q,ω)$ for the one-dimensional $s$=1/2 $XXZ$ model at $T$=0 in the antiferromagnetically ordered phase is calculated using recent advances by Jimbo and Miwa in the algebraic analysis based on (infinite-dimensional) quantum group symmetries of this model and the related vertex models. The 2-spinon excitations form a 2-parameter continuum consisting of two partly overlapping sheets in $(Q,ω)$-space. The spectral threshold has a smooth maximum at the Brillouin zone boundary $(Q=π/2)$ and a smooth minimum with a gap at the zone center $(Q=0)$. The 2-spinon density of states has square-root divergences at the lower and upper continuum boundaries. For the 2-spinon transition rates, the two regimes $0 \leq Q < Q_κ$ (near the zone center) and $Q_κ< Q \leq π/2$ (near the zone boundary) must be distinguished, where $Q_κ\to 0$ in the Heisenberg limit and $Q_κ\to π/2$ in the Ising limit. The resulting 2-spinon part of $S_{xx}(Q,ω)$ is then square-root divergent at the spectral threshold and vanishes in a square-root cusp at the upper boundary. In the regime $0 < Q_κ\leq π/2$, by contrast, the 2-spinon transition rates have a smooth maximum inside the continuum and vanish linearly at either boundary. Existing perturbation studies have been unable to capture the physics of the regime $Q_κ< Q \leq π/2$. However, their line shape predictions for the regime $0 \leq Q < Q_κ$ are in good agreement with the new exact results if the anisotropy is very strong.

cond-mat↗

arXiv1996

Charge and spin dynamics in the one-dimensional $t-J_z$ and $t-J$ models

The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the 1D $t-J$ model is assessed by comparison with the same quantities in the 1D $t-J_z$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At $J_z/t=0^+$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. The $t-J_z$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the $t-J$ model. In the $t-J_z$ model, phase separation is accompanied by Néel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the $t-J$ model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by 2-spinon excitations) in the phase-separated state.

cond-mat↗

arXiv1996

Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,ω)$ of he one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N\leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 72.89% of the total intensity in $S_{zz}(q,ω)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.

cond-mat↗

arXiv1996

Dimer and Néel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,ω) and S_{DD}(q,ω), which describe (for q=π) the fluctuations of the Néel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(π,ω) and S_{DD}(π,ω), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,ω) but not to S_{DD}(q,ω).

cond-mat↗

arXiv1995

Spin correlation functions in random-exchange s=1/2 XXZ chains

The decay of (disorder-averaged) static spin correlation functions at T=0 for the one-dimensional spin-1/2 XXZ antiferromagnet with uniform longitudinal coupling $JΔ$ and random transverse coupling $Jλ_i$ is investigated by numerical calculations for ensembles of finite chains. At $Δ=0$ (XX model) the calculation is based on the Jordan-Wigner mapping to free lattice fermions for chains with up to N=100 sites. At $Δ\neq 0$ Lanczos diagonalizations are carried out for chains with up to N=22 sites. The longitudinal correlation function $ $ is found to exhibit a power-law decay with an exponent that varies with $Δ$ and, for nonzero $Δ$, also with the width of the $λ_i$-distribution. The results for the transverse correlation function $ $ show a crossover from power-law decay to exponential decay as the exchange disorder is turned on.

cond-mat↗

arXiv1995

Order-parameter fluctuations in the frustrated Heisenberg model on the square lattice

The $T=0$ dynamics of the two-dimensional $s=1/2$ Heisenberg model with competing nearest-neighbor $(J_1)$ and next-nearest-neighbor $(J_2)$ interactions is explored via the recursion method, specifically the frequency-dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e. Néel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at $J_2/J_1 \gtrsim 0.6$ and a potential for dimer order at $0.5 \lesssim J_2/J_1 \lesssim 0.6$, whereas the chiral ordering tendency is observed to be considerably weaker.

cond-mat↗

arXiv1995

Impact of criticality and phase separation on the spin dynamics of the one-dimensional t-J model

The recursion method is used to determine the T=0 spin dynamic structure factor S_{zz}(q,ω) in the Luttinger liquid state and in the phase-separated state of the one-dimensional t-J model. As the exchange coupling increases from zero, the dispersions and line shapes of the dominant spin excitations are observed to undergo a major metamorphosis between the free-fermion limit and the onset of phase separation. The familiar two-spinon spectrum of the Heisenberg antiferromagnetic chain emerges gradually in the strongly phase-separated state.

cond-mat↗

arXiv1995

Dynamics of quantum spin systems in dimer and valence-bond solid ground states stabilized by competing interactions

For special coupling ratios, the one-dimensional (1D) s=1/2 Heisenberg model with antiferromagnetic nearest and next-nearest neighbor interactions has a pure dimer ground state, and the 1D s=1 Heisenberg model with antiferromagnetic bilinear and biquadratic interactions has an exact valence-bond-solid ground state. The recursion method is used to calculate the T=0 spin dynamic structure factor for both models and, for the s=1/2 model, also the dimer dynamic structure factor. New results for line shapes and dynamically relevant dispersions are obtained.

cond-mat↗

arXiv1995

Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

Dynamic spin correlation functions $ $ for the 1D $S=1/2$ $XX$ model $H = -JΣ_i \{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y \}$ are calculated exactly for finite open chains with up to N=10000 spins. Over a certain time range the results are free of finite-size effects and thus represent correlation functions of an infinite chain (bulk regime) or a semi-infinite chain (boundary regime). In the bulk regime, the long-time asymptotic decay as inferred by extrapolation is Gaussian at $T=\infty$, exponential at $0 < T < \infty$, and power-law $(\sim t^{-1/2})$ at T=0, in agreement with exact results. In the boundary regime, a power-law decay obtains at all temperatures; the characteristic exponent is universal at T=0 $(\sim t^{-1})$ and at $0 < T < \infty$ $(\sim t^{-3/2})$, but is site-dependent at $T=\infty$. In the high-temperature regime $(T/J \gg 1)$ and in the low-temperature regime $(T/J \ll 1)$, crossovers between different decay laws can be observed in $ $. Additional crossovers are found between bulk-type and boundary-type decay for $i=j$ near the boundary, and between space-like and time-like behavior for $i \neq j$.

cond-mat↗