The Trotter factorization of the Liouville propagator is used to generate new reversible molecular dynamics integrators This strategy is applied to derive reversible reference system propagator algorithms (RESPA) that greatly accelerate simulations of systems with a separation of time scales or with long range forces The new algorithms have all of the advantages of previous RESPA integrators but are reversible, and more stable than those methods These methods are applied to a set of paradigmatic systems and are shown to be superior to earlier methods It is shown how the new RESPA methods are related to predictor–corrector integrators Finally, we show how these methods can be used to accelerate the integration of the equations of motion of systems with Nose thermostats

/pdf/reversible-multiple-time-scale-molecular-dynamics-3vgrwfm9ig.pdf

Reversible multiple time scale molecular dynamics

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

/pdf/entanglement-in-many-body-systems-sqpatuxt14.pdf

Entanglement in many-body systems

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

Path integrals in the theory of condensed helium

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

Part I. Thermodynamics of Non-Interacting Systems and Ground States on Interacting Systems: 1. Free energy and correlation functions of XY models 2. Systems with delta-function potential 3. Isotropic Heisenberg model 4. XXZ model 5. XYZ and eight-vertex models 6. Hubbard model Part II. Finite Temperature Integral Equations for Un-Nested Systems: 7. Repulsive delta-function bosons 8. Thermodynamics of the XXX chain 9. Thermodynamics of the XXZ model 10. Thermodynamics of the XYZ model 11. Low-temperature thermodynamics Part III. Finite Temperature Integral Equations for Nested Systems: 12. S=1/2 fermions with repulsive potential in the continuum 13. S=1/2 fermions with an attractive potential 14. Thermodynamics of the Hubbard model Part IV. Quantum Transfer Matrix and Recent Developments: 15. Transfer matrix and correlation length 16. The spin 1/2 XXZ model in a magnetic field 17. The XYZ model with no magnetic field 18. Recent developments and related topics.

Thermodynamics of One-Dimensional Solvable Models

A modified spin-wave theory for the Heisenberg antiferromagnet (scrH=J) is formulated under the assumption of zero sublattice magnetization in the same way with the Heisenberg ferromagnet. This theory gives self-consistent equations which are equivalent to those of Auerbach and Arovas, but in our theory the factor of (3/2 in the correlation function does not appear. This theory reproduces the main results of traditional spin-wave theory, as well as those of renormalization-group theory, in a unified picture. For the square lattice at low temperature the susceptibility behaves as a+bT and the correlation length as (c/T)exp(d/T). This correlation length coincides very well with experimental results of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ if we choose J=900 K. Calculation of self-consistent equations is done for the S=(1/2 system and compared with the result of exact diagonalization of a 4\ifmmode\times\else\texttimes\fi{}4 system and high-temperature expansion. The quantitative agreement is surprisingly good, especially at T\ensuremath{\lesssim}0.6J. .AE

Modified spin-wave theory of a square-lattice antiferromagnet.

We discovered that an organic radical crystal, p-nitrophenyl nitronyl nitroxide (p-NPNN), is a quasi-1D ferromagnet induced by unpaired electrons on radicals. The magnetization and the susceptibility of the triclinic γ-phase crystal are very well represented by the Bethe-ansatz solution of the S=1/2 1D Heisenberg ferromagnet with nearest-neighbor coupling J⇒4.3 K. Low-temperature specific heat and ac susceptibility measurements revealed that the crystal undergoes a ferromagnetic transition at 0.65 K The interchain coupling J' was estimated to be about 0.1 K

Discovery of a quasi-1D organic ferromagnet, p-NPNN.

The higher order correction term is obtained for the Monte Carlo calculation of the path integral. The correction is expressed only by a modification of the potential term: $V(\textbf{\itshape r}_{1}, \cdots , \textbf{\itshape r}_{N}) \rightarrow V+(\hbar ^{2}/24m)(\beta /M)^{2} \sum _{i=1}^{N} (\partial V/\partial \textbf{\itshape r}_{i})^{2}$, where r i 's are coordinates of particles, N is number of particles with mass m , β is ( k T ) -1 and M is number of partitions. By this method one can reduce the computation time remarkably. A rapid convergence of energy is obtained for the case of harmonic oscillator.

Monte Carlo Calculation of Quantum Systems. II. Higher Order Correction

Glycosuria produced by sodium–glucose co-transporter-2 (SGLT-2) inhibitors is associated with weight loss. SGLT-2 inhibitors reportedly might reduce the occurrence of cardiovascular events. Epicardial adipose tissue (EAT) is a pathogenic fat depot that may be associated with coronary atherosclerosis. The present study evaluated the relationship between an SGLT-2 inhibitor (dapagliflozin) and EAT volume. In 40 diabetes mellitus patients with coronary artery disease (10 women and 30 men; mean age of all 40 patients was 67.2 ± 5.4 years), EAT volume was compared prospectively between the dapagliflozin treatment group (DG; n = 20) and conventional treatment group (CTG; n = 20) during a 6-month period. EAT was defined as any pixel that had computed tomography attenuation of − 150 to − 30 Hounsfield units within the pericardial sac. Metabolic parameters, including HbA1c, tumor necrotic factor-α (TNF-α), and plasminogen activator inhibitor-1 (PAI-1) levels, were measured at both baseline and 6-months thereafter. There were no significant differences at baseline of EAT volume and HbA1c, PAI-1, and TNF-α levels between the two treatment groups. After a 6-month follow-up, the change in HbA1c levels in the DG decreased significantly from 7.2 to 6.8%, while body weight decreased significantly in the DG compared with the CTG (− 2.9 ± 3.4 vs. 0.2 ± 2.4 kg, p = 0.01). At the 6-month follow-up, serum PAI-1 levels tended to decline in the DG. In addition, the change in the TNF-α level in the DG was significantly greater than that in the CTG (− 0.5 ± 0.7 vs. 0.03 ± 0.3 pg/ml, p = 0.03). Furthermore, EAT volume significantly decreased in the DG at the 6-month follow-up compared with the CTG (− 16.4 ± 8.3 vs. 4.7 ± 8.8 cm3, p = 0.01). Not only the changes in the EAT volume and body weight, but also those in the EAT volume and TNF-α level, showed significantly positive correlation. Treatment with dapagliflozin might improve systemic metabolic parameters and decrease the EAT volume in diabetes mellitus patients, possibly contributing to risk reduction in cardiovascular events.

/pdf/the-effect-of-dapagliflozin-treatment-on-epicardial-adipose-2wf1t8lfsv.pdf

Minoru Takahashi

Papers

Thermodynamics of One-Dimensional Solvable Models

Modified spin-wave theory of a square-lattice antiferromagnet.

Discovery of a quasi-1D organic ferromagnet, p-NPNN.

Monte Carlo Calculation of Quantum Systems. II. Higher Order Correction

The effect of dapagliflozin treatment on epicardial adipose tissue volume