Local Relaxation Rate Research Articles

Novel transition dynamics of topological solitons

Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but the latter is less understood. We fill this gap in knowledge by studying the transition dynamics to a parity-breaking topological ground state called the chiral soliton lattice in quantum chromodynamics at finite temperature, baryon chemical potential, and an external magnetic field. We find a slowing down of the soliton’s translational motion as the critical magnetic field approaches, while the local relaxation rate to the solitonic state remains finite. The time required to converge to the stationary state strongly depends on the symmetry of the initial configuration, determining whether translational motion occurs during the dynamic process. Published by the American Physical Society 2024

Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes -- different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster, or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This is caused by an exponential in system size explosion of expansion coefficient sizes resulting in a 'phantom' eigenvalue, and is due to non-orthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance also in other non-Hermitian settings, including correlations.

Effects of mesoscopic susceptibility and transverse relaxation on diffusion NMR

Measuring molecular diffusion is based on the spatial encoding of spin-carrying molecules using external Larmor frequency gradients. Intrinsic variations of the Larmor frequency and of the local relaxation rate, commonly present in structurally complex samples, interfere with the external gradients, confounding the NMR-measured diffusion propagator. Here we consider, analytically and numerically, the effects of the mesoscopic magnetic structure (local susceptibility and transverse relaxation rate) on the NMR-measured “apparent” diffusion coefficient (ADC). We show that in the fast diffusion regime, when molecules spread past the correlation length of the magnetic structure, the deviation of ADC from the genuine diffusion coefficient increases as a power law of diffusion time. The effect of mesoscopically varying transverse relaxation rate is sequence-independent and always leads to the decrease of ADC with time, whereas the effect sign for the mesoscopic Larmor frequency variations depends on the presence of refocussing pulses in the diffusion sequence. We connect this unexpectedly diverging with time ADC discrepancy to the spatial statistics of the mesocopic magnetic structure. Our results establish a novel kind of NMR contrast tied to the microstructural complexity, and can be applied to discern the mesoscopic effects of hindrances to molecular diffusion, susceptibility variations, and varying local relaxation rate, on the measured diffusion propagator. In particular, we numerically show that the susceptibility effect of a microvascular network is sufficient to explain the observed ADC decrease due to superparamagnetic iron-oxide contrast injection in monkeys.

Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases.

We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.

CPMG relaxation rate dispersion in dipole fields around capillaries

Transverse relaxation rates for Carr-Purcell-Meiboom-Gill (CPMG) sequences increase with inter-echo time in presence of microscopic magnetic field inhomogeneities due to nuclear spin diffusion. For a weak field approximation that includes diffusion effects, the CPMG relaxation rate shift for proton diffusion around capillaries in muscle tissue can be expressed in terms of a frequency correlation function and the inter-echo time. The present work provides an analytical expression for the local relaxation rate shift that is dependent on local blood volume fraction, diffusion coefficient, capillary radius, susceptibility difference and inter-echo time. Asymptotic regions of the model are in agreement with previous modeling results of Brooks et al., Luz et al. and Ziener et al. In comparison with simulation data, the model shows an equal or better accuracy than established approximations. Also, model behavior coincides with experimental data for rat heart and skeletal muscle. The present work provides analytical tools to extract sub-voxel information about uniform capillary networks that can be used to study capillary organization or micro-circulatory remodeling.

Comment on “An improved gray Lattice Boltzmann model for simulating fluid flow in multi-scale porous media”: Intrinsic links between LBE Brinkman schemes

In this Comment on the recent work (Zhu and Ma, 2013) [11] by Zhu and Ma (ZM) we first show that all three local gray Lattice Boltzmann (GLB) schemes in the form (Zhu and Ma, 2013) [11]: GS (Chen and Zhu, 2008; Gao and Sharma, 1994) [1,4], WBS (Walsh et al., 2009) [12] and ZM, fail to get constant Darcy’s velocity in series of porous blocks. This inconsistency is because of their incorrect definition of the macroscopic velocity in the presence of the heterogeneous momentum exchange, while the original WBS model (Walsh et al., 2009) [12] does this properly. We improve the GS and ZM schemes for this and other related deficiencies. Second, we show that the “discontinuous velocity” they recover on the stratified interfaces with their WBS scheme is inherent, in different degrees, to all LBE Brinkman schemes, including ZM scheme. None of them guarantees the stress and the velocity continuity by their implicit interface conditions, even in the frame of the two-relaxation-times (TRT) collision operator where these two properties are assured in stratified Stokes flow, Ginzburg (2007) [5]. Third, the GLB schemes are presented in work (Zhu and Ma, 2013) [11] as the alternative ones to direct, Brinkman-force based (BF) schemes (Freed, 1998; Nie and Martys, 2007) [3,8]. Yet, we show that the BF-TRT scheme (Ginzburg, 2008) [6] gets the solutions of any of the improved GLB schemes for specific, viscosity-dependent choice of its one or two local relaxation rates. This provides the principal difference between the GLB and BF: while the BF may respect the linearity of the Stokes–Brinkman equation rigorously, the GLB-TRT cannot, unless it reduces to the BF via the inverse transform of the relaxation rates. Furthermore, we show that, in limited parameter space, “gray” schemes may run one another. From the practical point of view, permeability values obtained with the GLB are viscosity-dependent, unlike with the BF. Finally, the GLB shares with the BF a so-called anisotropy (Ginzburg, 2008; Nie and Martys, 2007) [6,8], that is, flow-direction-dependency in their effective viscosity corrections, related to the discretized spatial variation of the resistance forcing.

Communication: A minimal model for the diffusion-relaxation backbone dynamics of proteins

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.

Polymer Chain Dynamics in a Random Environment: Heterogeneous Mobilities

We present a neutron scattering investigation on a miscible blend of two polymers with greatly different glass-transition temperatures Tg. Under such conditions, the nearly frozen high-Tg component imposes a random environment on the mobile chain. The results demand the consideration of a distribution of heterogeneous mobilities in the material and demonstrate that the larger scale dynamics of the fast component is not determined by the average local environment alone. This distribution of mobilities can be mapped quantitatively on the spectrum of local relaxation rates measured at high momentum transfers.

Two-body relaxation in cold dark matter simulations

N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialized objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then attempt to determine how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few per cent of the final structures - a region that one might naively think is well resolved at the final time since the haloes contain 10 6 particles - suffer from high degrees of relaxation. It is not clear how to interpret the effects of the accumulated relaxation rate, but we argue thai it describes a region within which one should be careful about trusting the numerical results. Substructure haloes are most affected by relaxation since they contain few particles at a constant energy for the entire simulation. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation, and we find that increasing N slowly reduces the degree of relaxation oc N -0.25 rather than proportional to N as expected from the collisionless Boltzmann equation. Simulated with the same relative mass resolution (i.e. equal numbers of particles), cluster mass objects suffer significantly more relaxation than galaxy mass objects since they form relatively late and therefore more of the particles spend more time in small-N haloes.

Conduction in molecular junctions: inelastic effects

The effect of a thermal environment on electron (or hole) transfer through molecular bridges and on the electron conduction properties of such bridges is studied. Our steady state formalism based on an extension of the Redfield theory [J. Phys. Chem. B 104 (2000) 3817; Chem. Phys. 268 (2001) 315] is extended in two ways: First, a better description of the weak-coupling limit, which accounts for the asymmetry of the energy dependence of the quasi-elastic component of the transmission is employed. Secondly, for strong coupling to the thermal bath the small polaron transformation is employed prior to the Redfield expansion. It is shown that the thermal coupling is mainly characterized by two physical parameters: the reorganization energy that measures the coupling strength and the correlation time (or its inverse – the spectral width) of the thermal bath. Implications for the observed dependence of the bridge-length dependence of the transmissions are discussed. It is argued that in the intermediate regime between tunneling behavior and site-to-site thermally induced hopping, the transport properties may depend on the interplay between the local relaxation rate and the transmission dynamics.

Properties of the manganese(II) binding site in ternary complexes of manganese.cntdot.ADP and manganese.cntdot.ATP with chloroplast coupling factor 1: magnetic field dependence of solvent proton and deuterium NMR relaxation rates

The influence of the binding of ADP and ATP on the high-affinity Mn(II) binding site of chloroplast coupling factor 1 (CF{sub 1}) was studied by analysis of field-dependent solvent proton and deuteron spin-lattice relaxation data. In order to characterize metal-nucleotide complexes of CF{sub 1} under conditions similar to those of the NMR experiments, the enzyme was analyzed for bound nucleotides and Mn(II) after incubation with AdN and MnCl{sub 2} and removal of labile ligands by extensive gel filtration chromatography. In the field-dependent NMR experiments, the Mn(II) binding site of CF{sub 1} was studied for three mole ratios of added Mn(II) to CF{sub 1}, 0.5, 1.0, and 1.5, in the presence of an excess of either ADP or ATP. The results were extrapolated to zero Mn(II) concentration to characterize the environment of the first Mn(II) binding site of Cf{sub 1}. In the presence of both adenine nucleotides, pronounced changes in the Mn(II) environment relative to that in Mn(II)-CF{sub 1} were evident; the local relaxation rate maxima were more pronounced and shifted to higher field strengths, and the relaxation rate per bound Mn(II) increased at all field strengths. Analysis of the data revealed that the number of exchangeable water molecules liganded tomore » bound Mn(II) increased from one in the binary Mn(II)-CF{sub 1} complex to three and two in the ternary Mn(II)-ADP-CF{sub 1} and Mn(II)-ATP-CF{sub 1} complexes, respectively; these results suggest that a water ligand to bound Mn(II) in the Mn(II)-ADP-CF{sub 1} complex is replaced by the {gamma}-phosphate of ATP in the Mn(II)-ATP-CF{sub 1} complex. A binding model is presented to account for these observations.« less

Solvent induced vibrational relaxation in diatomics. I. Derivation of a local relaxation rate

A local rate is derived for the vibrational population relaxation of a diatomic in a simple liquid or dense gas. The total relaxation rate of the system is obtained as the canonical ensemble average of the local rate. The rate expression is amenable to computer simulations in which the canonical average is performed by a Monte Carlo procedure. The vibrational motion is separated from the other degrees of freedom by an adiabatic approximation which treats the vibration as fast compared with the other motions. The adiabatic vibrational energies and the nonadiabatic couplings between vibrational states depend on the solvent configuration. These vibrational energies and couplings are obtained from quantum perturbation theory. The transitions between vibrational states are described semiclassically and the canonical averaging uses the classical canonical density for solvent configurations. The resulting procedure is a mixed quantum–semiclassical–classical simulation technique.

Dynamics of compatible polymer mixtures

We discuss the mutual diffusion of a compatible molten mixture A + B assuming that the chains are flexible and relatively short (non-entangled). In the macroscopic limit the mutual diffusion coefficient D m is predicted to be extremely large (independent of the molecular weights). When we go to shorter wave vectors q two cross-overs occur: 1. a) when the frequency D m q 2 becomes larger than the fundamental Rouse time T R of a single chain, the coefficient D m becomes q dependent, D m → D m ( q ) ∼ q 2 ; 2. b) when the spatial scales become smaller than the coil size R 0 ( qR 0 1) the width D m ( q)q 2 becomes independent of q , and is comparable to a local relaxation rate. These predictions could be tested by a combination of photon beat and neutron quasi elastic scattering.

Estimation of the Influence of Lattice Resonant Modes on the Nuclear Quadrupole Spin–Lattice Relaxation

AbstractThe influence of nonparamagnetic point and line defects in the crystal lattice on the nuclear quadrupole spin‐lattice relaxation is studied. Under the assumption of simple models for defects in a cubic lattice it is shown that lattice resonant modes cause at low temperature an increase of the local relaxation rate around the defects. The efficiency of spin diffusion is estimated. Measurable effects are expected only with relatively high concentrations of defects.