We reexamine mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling limit and show that there exist two branches of solutions. One branch (or universality class) exists only for dimensionalities $d<d_c=2$ and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to $d_c=4$ and gives values for the dynamical exponent $z$ similar to those of numerical studies for $d\ge 2$.

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with an identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar.

We present a theory to describe domain formation observed very recently in a quenched ${}^{87}\mathrm{Rb}$ gas, a typical ferromagnetic spinor Bose system. An overlap factor is introduced to characterize the symmetry breaking of $M_F=\pm 1$ components for the $F=1$ ferromagnetic condensate. We demonstrate that the domain formation is a coeffect of the quantum coherence and the thermal relaxation. A thermally enhanced quantum oscillation is observed during the dynamical process of the domain formation. And the spatial separation of domains leads to significant decay of the $M_F=0$ component fraction in an initial $M_F=0$ condensate.

A Bayesian framework is developed to reconstruct the density of states from multiple canonical simulations. The framework encompasses the histogram reweighting method of Ferrenberg and Swendsen. The new approach applies to nonparametric as well as parametric models and does not require simulation data to be discretized. It offers a means to assess the precision of the reconstructed density of states and of derived thermodynamic quantities.

We show that in finite dimensions a quantum measurement with a continuous set of outcomes can be always realized as a continuous random choice of measurements with a finite number of outcomes.

We show that quantum and thermal fluctuations in spin-2 Bose-Einstein condensates lift the accidental degeneracy of the mean-field phase diagram. Fluctuations select the uniaxial (square biaxial) nematic state for scattering lengths $a_4>a_2$ ($a_4<a_2$). Paradoxically, the order is stronger at higher temperatures. For spin-2 ${}^{87}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}$, a continuous Ising-type transition is predicted on raising the magnetic field, from a fluctuation stabilized uniaxial state to a field stabilized square biaxial order state. This is a promising experimental system to realize the “order-by-disorder” phenomenon.

We propose a quantum repeater protocol which builds on the well-known Duan-Lukin-Cirac-Zoller (DLCZ) protocol [L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature (London) 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multimode memories based on the principle of photon echo, using solids doped with rare-earth-metal ions. The use of multimode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.

We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate, storage, and measurement errors.

NMR spin echo measurements of ${}^{13}\mathrm{C}$ in ${\mathrm{C}}_{60}$, ${}^{89}\mathrm{Y}$ in ${\mathrm{Y}}_2{\mathrm{O}}_3$, and ${}^{29}\mathrm{Si}$ in silicon are shown to defy conventional expectations when more than one $\pi$ pulse is used. Multiple $\pi$-pulse echo trains may either freeze out or accelerate the decay of the signal, depending on the $\pi$-pulse phase. Average Hamiltonian theory, combined with exact quantum calculations, reveals an intrinsic cause for these coherent phenomena: the dipolar coupling has a many-body effect during any real, finite pulse.

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.

We have performed quantum molecular dynamics simulations for dense helium to study the nonmetal-to-metal transition at high pressures. We present new results for the equation of state and the Hugoniot curve in the warm dense matter region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity is derived. The nonmetal-to-metal transition is identified at about $1\mathrm{g}/{\mathrm{cm}}^3$. We compare with experimental results as well as with other theoretical approaches, especially with predictions of chemical models.

We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlation functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms.

Khinchin’s theorem of ergodicity is examined by means of linear response theory. The resulting ergodic condition shows that, contrary to the theorem, irreversibility is not a sufficient condition for ergodicity. By the recurrence relations method, we prove that irreversibility is broader in scope than ergodicity, showing why it can only be a necessary condition for ergodicity.

We show that, for experimentally relevant systems, there is an optimal measurement strategy to monitor the time evolution of entanglement under open system dynamics. This suggests an efficient, dynamical characterization of the entanglement of composite, open quantum systems.

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution $n(\mathbf{k})$ can be misleading, for even a normal Bose gas can have a similarly sharp $n(\mathbf{k})$. We show that superfluidity in a homogeneous system can be detected from the so-called visibility ($v$) of $n(\mathbf{k})$—that $v$ must be 1 within $O(N^{-2/3})$, where $N$ is the number of bosons. We also show that the $T=0$ visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.

We report on the experimental realization of a four-qubit linear cluster state via two photons entangled both in polarization and linear momentum. This state was investigated by performing tomographic measurements and by evaluating an entanglement witness. By use of this state we carried out a novel nonlocality proof, the so-called “stronger two observer all-versus-nothing” test of quantum nonlocality.

We create independent, synchronized single-photon sources with built-in quantum memory based on two remote cold atomic ensembles. The synchronized single photons are used to demonstrate efficient generation of entanglement. The resulting entangled photon pairs violate a Bell’s inequality by 5 standard deviations. Our synchronized single photons with their long coherence time of 25 ns and the efficient creation of entanglement serve as an ideal building block for scalable linear optical quantum information processing.

We describe a novel switching algorithm based on a “reverse” Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to ${1024}^2$ were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.

We consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force. The force breaks detailed balance, maintained otherwise, thus producing entropy. The large deviation function of the entropy production in the system is calculated explicitly. The general result is illustrated using an example of a polymer immersed in a gradient flow and subject to thermal fluctuations.

We study the electric potential of a charge placed in a strong magnetic field $B\gg B_0\simeq 4.4\times {10}^{13}\mathrm{G}$, as modified by the vacuum polarization. In such a field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across $\mathbf{B}$ faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit $B=\infty$, the modified potential becomes the Dirac $\delta$ function plus a regular background. With this potential the ground-state energy is finite—the best pronounced effect of the vacuum polarization.