arXiv subjects

R. Schilling

Publications and source records attributed to R. Schilling.

At least 37 records · Page 2Linked to original sources

arXiv2006

Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions

We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of α_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a nonuniversal one, involving the full time dependence of E_(+-)(t). This general result is applied to the Akulin-Schleich model where the initial upper level is damped with damping constant $γ$. For analytic power-law sweeps we find that Stueckelberg oscillations of P exist for gamma smaller than a critical value gamma_c and disappear for gamma > gamma_c. A physical interpretation of this behavior will be presented by use of a damped harmonic oscillator.

quant-ph↗

arXiv2005

Glassy behavior of molecular crystals: A comparison between results from MD-simulation and mode coupling theory

We have investigated the glassy behavior of a molecular crystal built up with chloroadamantane molecules. For a simple model of this molecule and a rigid fcc lattice a MD simulation was performed from which we obtained the dynamical orientational correlators $S_{λλ'}({\bf{q}},t)$ and the ``self'' correlators $S_{λλ'}^{(s)}(t)$, with $λ= (\ell, m)$, $λ' = (\ell', m')$. Our investigations are for the diagonal correlators $λ= λ'$. Since the lattice constant decreases with decreasing temperature which leads to an increase of the steric hindrance of the molecules, we find a strong slowing down of the relaxation. It has a high sensitivity on $λ$, $λ'$. For most $(\ell,m)$, there is a two-step relaxation process, but practically not for $(\ell,m) = (2,1)$, $(3,2)$, $(4,1)$ and $(4,3)$. Our results are consistent with the $α$-relaxation scaling laws predicted by mode coupling theory from which we deduce the glass transition temperature $T_c^{MD} \cong 217K$. From a first principle solution of the mode coupling equations we find $T_c^{MCT} \cong 267K$. Furthermore mode coupling theory reproduces the absence of a two-step relaxation process for $(\ell,m)=(2,1)$, $(3,2)$, $(4,1)$ and $(4,3)$, but underestimates the critical nonergodicity parameters by about 50 per cent for all other $(\ell,m)$. It is suggested that this underestimation originates from the anisotropic crystal field which is not accounted for by mode coupling theory. Our results also imply that phonons have no essential influence on the long time relaxation.

cond-mat.soft↗

arXiv2005

Universal mechanism of spin relaxation in solids

We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.

cond-mat.stat-mech↗

arXiv2005

Many-body Landau-Zener effect at fast sweep

The asymptotic staying probability P in the Landau-Zener effect with interaction is analytically investigated at fast sweep, epsilon = pi Delta^2/(2 hbar v) << 1. We have rigorously calculated the value of I_0 in the expansion P =~ 1 - epsilon + epsilon^2/2 + epsilon^2 I_0 for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction (DDI) generate huge values of I_0 because flip of one particle strongly influences many others. However, in the presence of strong static disorder making resonance for individual particles shifted with respect to each other the influence of interactions is strongly reduced. In molecular magnets the main source of static disorder is the coupling to nuclear spins. Our calculations using the actual shape of the Fe-8 crystal studied in the the Landau-Zener experiments [Wernsdorfer et al, Europhys. Lett. 50, 552 (2000)] yield I_0 that is in a good agreement with the value extracted from the experimental data.

cond-mat.stat-mech↗

arXiv2004

Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model

We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $α_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1, provided that the interaction strength mu is smaller than a critical value. The saddle index n_s is equal to alpha_0 and its distribution function has a maximum at n_s^max = 1/3. The density p(e) of stationary points with energy per particle e, as well as the Euler characteristic chi(e), are singular at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu) \neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per particle at the thermodynamic phase transition point T_c. This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H \neq 0. The average saddle index bar{n}_s as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 > upsilon_0, the ground state energy.

cond-mat.stat-mech↗

arXiv2004

Frequency domain interferometer simulation with higher-order spatial modes

FINESSE is a software simulation that allows to compute the optical properties of laser interferometers as they are used by the interferometric gravitational-wave detectors today. It provides a fast and versatile tool which has proven to be very useful during the design and the commissioning of gravitational-wave detectors. The basic algorithm of FINESSE numerically computes the light amplitudes inside an interferometer using Hermite-Gauss modes in the frequency domain. In addition, FINESSE provides a number of commands to easily generate and plot the most common signals like, for example, power enhancement, error or control signals, transfer functions and shot-noise-limited sensitivities. Among the various simulation tools available to the gravitational wave community today, FINESSE is the most advanced general optical simulation that uses the frequency domain. It has been designed to allow general analysis of user defined optical setups while being easy to install and easy to use.

gr-qc↗

arXiv2003

Transitions at avoided level crossing with interaction and disorder

We investigate the influence of interaction between tunneling particles and disorder on their avoided-level-crossing transitions in the fast-sweep limit. Whereas the results confirm expectations based on the mean-field arguments that ferromagnetic/antiferromagnetic couplings suppress/enhance transitions, we found large deviations from the mean-field behavior for dipole-dipole interactions (DDI) in molecular magnets Mn-12 and Fe-8. For ideal crystals of the needle, spherical, and disc shapes DDI tends to enhance transitions. This tendency is inverted for the needle shape in the presence of even small disorder in the resonance fields of individual particles, however.

cond-mat.stat-mech↗

arXiv2003

Quantum Nonlinear Switching Model

We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model \hat{H} = -H_z(t)S_z + V(\bf{S}) with H_z(\pm\infty) = \pm\infty and Ψ(-\infty)=|-S> we study the quantity P(t)=(1- _t/S)/2. The case V(\bf{S})=-H_x S_x corresponds to the standard Landau-Zener-Stueckelberg model of tunneling at avoided-level crossing for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and follows, e.g., from the classical Landau-Lifshitz equation. A term -DS_z^2 accounts for particles' interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in a good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0.

cond-mat.stat-mech↗

arXiv2002

Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect

We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability P to remain in the initial state. The dimensionless quantity epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and monotonic, analytic sweep functions linearizable in the vicinity of the resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is the correction to the LSZ result due to the nonlinearity of the sweep. Further increase of the sweep rate with nonlinearity fixed brings the system into the nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1 depending on the type of sweep function. In case of slow sweep rates, i.e., epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t) the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta ^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there is only one singularity, that leads to the LZS result P=e^-epsilon with important corrections to the exponent due to nonlinearity. However, for, e.g., W(t) ~ t^3 there is a pair of singularities in the upper complex plane. Interference of their contributions leads to oscillations of the prefactor P_0 that depends on the sweep rate through epsilon and turns to zero at some epsilon. Measurements of the oscillation period and of the exponential factor would allow to determine Delta, independently.

cond-mat.stat-mech↗

arXiv2002

Inverse problem for the Landau-Zener effect

We consider the inverse Landau-Zener problem which consists in finding the energy-sweep functions W(t)=E1(t)-E2(t) resulting in the required time dependences of the level populations for a two-level system crossing the resonance one or more times during the sweep. We find sweep functions of particular forms that let manipulate the system in a required way, including complete switching from the state 1 to the state 2 and preparing the system at the exact ground and excited states at resonance.

cond-mat.stat-mech↗

arXiv2001

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin.

cond-mat.dis-nn↗

arXiv2001

Microscopic Dynamics of Hard Ellipsoids in their Liquid and Glassy Phase

To investigate the influence of orientational degrees of freedom onto the dynamics of molecular systems in its supercooled and glassy regime we have solved numerically the mode-coupling equations for hard ellipsoids of revolution. For a wide range of volume fractions $ϕ$ and aspect ratios $x_{0}$ we find an orientational peak in the center of mass spectra $χ_{000}^{''}(q,ω)$ and $ϕ_{000}^{''} (q,ω)$ about one decade below a high frequency peak. This orientational peak is the counterpart of a peak appearing in the quadrupolar spectra $χ_{22m}^{''}(q,ω)$ and $ϕ_{22m}^{''}(q,ω)$. The latter peak is almost insensitive on $ϕ$ for $x_{0}$ close to one, i.e. for weak steric hindrance, and broadens strongly with increasing $x_{0}$. Deep in the glass we find an additional peak between the orientational and the high frequency peak. We have evidence that this intermediate peak is the result of a coupling between modes with $l=0$ and $l=2$, due to the nondiagonality of the static correlators.

cond-mat.dis-nn↗

arXiv2001

Microscopic dynamics of molecular liquids and glasses: Role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phase, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior which ranges from a simple hard sphere fluid to a long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra $ϕ_{lm}^{\prime \prime}(q,ω)$ and $χ_{lm}''(q,ω)$. In the center of mass spectra $ ϕ_{00}''(q,ω)$ and $χ_{00}''(q,ω)$ we found besides a high frequency peak at $ω_{hf}$ a peak at $ω_{op}$, about one decade below $ω_{hf}$. $ω_{op}$ has almost no $q$-dependence and exhibits an ``isotope'' effect $ω_{op}\propto I^{-1/2}$, with $I$ the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of the medium ranged orientational order. It is shown that some of these feature also exist for schematic mode coupling models.

cond-mat.dis-nn↗

arXiv2000

Demonstration of detuned dual recycling at the Garching 30m laser interferometer

Dual recycling is an advanced optical technique to enhance the signal-to-noise ratio of laser interferometric gravitational wave detectors in a limited bandwidth. To optimise the center of this band with respect to Fourier frequencies of expected gravitational wave signals detuned dual recycling has to be implemented. We demonstrated detuned dual recycling on a fully suspended 30m prototype interferometer. A control scheme that allows to tune the detector to different frequencies will be outlined. Good agreement between the experimental results and numerical simulations has been achieved.

gr-qc↗

arXiv2000

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $β$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cut off on the non ergodicity parameter, we also calculate the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we also propose a new method for the calculation of the critical nonergodicity parameter

cond-mat.dis-nn↗

arXiv2000

Ideal glass transitions for hard ellipsoids

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X$_0$. With increasing aspect ratio we find the idealized glass transition to become primarily be driven by orientational degrees of freedom. For needle or plate like systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition lines. The first one ($ϕ_c^{(B)}$) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one ($ϕ_c^{(B')}$) which occurs for rather non-spherical particles a glass phase is formed which consists of domains. Within each domain there is a nematic order where the center of mass motion is quasi--ergodic, whereas the inter--domain orientations build an orientational glass. The third glass transition line ($ϕ_c^{(A)}$) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g. 180$^o$ flips, freeze independently from the positions.

cond-mat.soft↗

arXiv2000

Test of molecular mode coupling theory: A first resume

We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass transition temperature $T_c$ is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the "full" set of MMCT-equations truncated at $l_{co}=2$. These results are compared $(i)$ with the nonergodicity parameters from MMCT with $l_{co}=2$ in the "dipole" approximation $n=n'=0$ and the diagonalization approximation $n=n'=0$,$l=l'$ and $(ii)$ with the corresponding results from a MD-simulation. This work supports the possibility that a reduction to the most prominent correlators may constitute a valid approximation for solving the MMCT equations for rigid molecules.

cond-mat.soft↗

arXiv2000

Molecular Correlations in a Supercooled Liquid

We present static and dynamic properties of molecular correlation functions S_{lmn,l'm'n'}(q,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions which can be predicted on the basis of the C_{2v}-symmetry of the molecule. The analysis of the MD--results for the static correlators S_{lmn,l'm'n'}(q) reveals that additional relationships between correlators with different signs of n and n' exist. We prove that for molecules with C_{rv}-symmetry this unexpected result becomes exact at least for high temperatures.

cond-mat.stat-mech↗