Environment-induced uncertainties on moving mirrors in quantum critical theories via holography

Environment effects on a $n$-dimensional mirror from the strongly coupled d-dimensional quantum critical fields with a dynamic exponent $z$ in weakly squeezed states are studied by the holographic approach. The dual description is a $n+1$-dimensional probe brane moving in the $d+1$-dimensional asymptotic Lifshitz geometry with gravitational wave perturbations. Using the holographic influence functional method, we find that the large coupling constant of the fields reduces the position uncertainty of the mirror, but enhances the momentum uncertainty. As such, the product of the position and momentum uncertainties is independent of the coupling constant. The proper choices of the phase of the squeezing parameter might reduce the uncertainties, nevertheless large values of its amplitude always lead to the larger uncertainties due to the fact that more quanta are excited as compared with the corresponding normal vacuum and thermal states. In the squeezed vacuum state, the position and momentum of the mirror gain maximum uncertainties from the field at the dynamic exponent $z=n+2$ when the same squeezed mode is considered. As for the squeezed thermal state, the contributions of thermal fluctuations to the uncertainties decrease as the temperature increases in the case $1n+2$ the contributions increase as the temperature increases. These results are in sharp contrast with those in the environments of the relativistic free field. Some possible observable effects are discussed.Comment: This is the version (v2) published in the Annals of Physic

Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields

The evolution of the Von Neumann entanglement entropy of a $n$-dimensional mirror influenced by the strongly coupled $d$-dimensional quantum critical fields with a dynamic exponent $z$ is studied by the holographic approach. The dual description is a $n+1$-dimensional probe brane moving in the $d+1$-dimensional asymptotic Lifshitz geometry ended at $r=r_b$, which plays a role as the UV energy cutoff. Using the holographic influence functional method, we find that in the linear response region, by introducing a harmonic trap for the mirror, which serves as a IR energy cutoff, the Von Neumann entropy at late times will saturate by a power-law in time for generic values of $z$ and $n$. The saturated value and the relaxation rate depend on the parameter $\alpha\equiv 1+(n+2)/z$, which is restricted to $1<\alpha <3$ but $\alpha \ne 2$. We find that the saturated values of the entropy are qualitatively different for the theories with $1<\alpha<2$ and $2<\alpha<3$. Additionally, the power law relaxation follows the rate $\propto t^{-2\alpha-1}$. This probe brane approach provides an alternative way to study the time evolution of the entanglement entropy in the linear response region that shows the similar power-law relaxation behavior as in the studies of entanglement entropies based on Ryu-Takayanagi conjecture. We also compare our results with quantum Brownian motion in a bath of relativistic free fields.Comment: The published versio

Subvacuum effects in Quantum Critical Theories from Holographic Approach

Subvacuum phenomena on a massive particle induced by a squeezed vacuum state of strongly coupled critical fields with a dynamical scaling $z$ are studied by employing the holographic approach. The corresponding dual description is the string moving in the 4+1-dimensional Lifshitz geometry. The squeezed vacuum state is constructed from the Bogoliubov transformations of the creation and annihilation operators of the pure vacuum state as a result from the perturbed geometry. Then the influence on particle's velocity dispersion from the squeezed vacuum is studied. With appropriate choices of squeezing parameters, the velocity dispersion is found smaller than the value caused by the normal vacuum fluctuations. This leads to a subvacuum effect. We find that the reduction in the velocity dispersion is suppressed by a large coupling constant of quantum critical fields, but is in principle observable. We then investigate the effect of the squeezed vacuum to the decoherence dynamics of a quantum particle. It is found possible for this decoherence to be below the level from the pure vacuum, rendering another subvacuum phenomenon of recoherence. We make some estimates of the degree of recoherence, and show that, in contrary to the velocity dispersion, the recoherence effect is proportional to the large coupling constant, and can potentially be observed. Finally we make a comparison with the effect on the particle influenced by a relativistic free field with the dynamical scaling $z=1$.Comment: This is the version (v2) published in PR

Notes on Properties of Holographic Strange Metals

We investigate properties of holographic strange metals in $p+2$-dimensions, generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is $p+2$-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density, the heat capacity as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.Comment: 32 pages, minor modification

A Holographic Description of Negative Energy States

Using the AdS/CFT duality, we study the expectation value of stress tensor in $2+1$-dimensional quantum critical theories with a general dynamical scaling $z$, and explore various constrains on negative energy density for strongly coupled field theories. The holographic dual theory is the theory of gravity in 3+1-dimensional Lifshitz backgrounds. We adopt a consistent approach to obtain the boundary stress tensor from bulk construction, which satisfies the trace Ward identity associated with Lifshitz scaling symmetry. In particular, the boundary stress tensor, constructed from the gravitational wave deformed Lifshitz geometry, is found up to second order in gravitational wave perturbations. {The result} is compared to its counterpart in free {scalar} field theory at the same order in an expansion of small squeezing parameters. This allows us to relate the boundary values of gravitational waves to the squeezing parameters of squeezed vacuum states. We find that, in both cases with $z=1$, the stress tensor satisfies the averaged null energy condition, and is consistent with the quantum interest conjecture. Moreover, the negative lower bound on null-contracted stress tensor, which is averaged over time-like trajectories along nearly null directions, is obtained. We find a weaker constraint on the magnitude and duration of negative null energy density in strongly coupled field theory as compared with the constraint in free relativistic field theory. The implications are discussed.Comment: This is the version(v2) published in JHE

Off-equilibrium dynamics of the primordial perturbations in the inflationary universe: the O(N) model

Using the O(N) model as an example, we investigate the self-interaction effects of inflaton on the dynamics of the primordial perturbations. When taking interactions into account, it is essential to employ a self-consistent off-equilibrium formalism to study the evolution of the inflationary background field and its fluctuations with the back-reaction effects. Within the Hartree factorization scheme, we show that the O(N) model has at least two observable remains left behind the off-equilibrium processes: the running spectral index of primordial density perturbations and the correlations between perturbation modes in phase space. We find that the running of the spectral index is fully determined by the rate of the energy transfer from the inflationary background field to its fluctuations via particle creation processes as well as the dynamics of the background field itself. Furthermore, the amplitude of the field fluctuations turns out to be scale-dependent due to the off-equilibrium evolution. As a consequence, the scale-dependence of fluctuations yields a correlation between the phase space modes of energy density perturbations, while the one-point function of the fluctuations in each Hartree mode is still Gaussian. More importantly, the mode-mode correlation of the primordial perturbations depends upon the dynamics of the self-interaction {\it as well as} the initial conditions of the inflation. Hence, we propose that the running spectral index and the correlation between phase-space modes would be two observable fossils to probe the epoch of inflation, even beyond.Comment: 22 pages, 8 figure

Perfect digraphs

Let $D$ be a digraph. Given a set of vertices $S \subseteq V(D)$, an $S$-path partition $\mathcal{P}$ of $D$ is a collection of paths of $D$ such that $\{V(P) \colon P \in \mathcal{P}\}$ is a partition of $V(D)$ and $|V(P) \cap S| = 1$ for every $P \in \mathcal{P}$. We say that $D$ satisfies the $\alpha$-property if, for every maximum stable set $S$ of $D$, there exists an $S$-path partition of $D$, and we say that $D$ is $\alpha$-diperfect if every induced subdigraph of $D$ satisfies the $\alpha$-property. A digraph $C$ is an anti-directed odd cycle if (i) the underlying graph of $C$ is a cycle $x_1x_2 \cdots x_{2k + 1}x_1$, where $k \in \mathbb{Z}$ and $k \geq 2$, and (ii) each of the vertices $x_1, x_2, x_3, x_4, x_6,$ $x_8, \ldots, x_{2k}$ is either a source or a sink. Berge (1982) conjectured that a digraph is $\alpha$-diperfect if, and only if, it contains no induced anti-directed odd cycle. Remark that this conjecture is strikingly similar to Berge's conjecture on perfect graphs -- nowadays known as the Strong Perfect Graph Theorem (Chudnovsky, Robertson, Seymour, and Thomas, 2006). To the best of our knowledge, Berge's conjecture for $\alpha$-diperfect digraphs has been verified only for symmetric digraphs and digraphs whose underlying graph are perfect. In this paper, we verify it for digraphs whose underlying graphs are series-parallel and for in-semicomplete digraphs. Moreover, we propose a conjecture similar to Berge's and verify it for all the known cases of Berge's conjecture

Interactive Graphics for Visually Diagnosing Forest Classifiers in R

This paper describes structuring data and constructing plots to explore forest classification models interactively. A forest classifier is an example of an ensemble, produced by bagging multiple trees. The process of bagging and combining results from multiple trees, produces numerous diagnostics which, with interactive graphics, can provide a lot of insight into class structure in high dimensions. Various aspects are explored in this paper, to assess model complexity, individual model contributions, variable importance and dimension reduction, and uncertainty in prediction associated with individual observations. The ideas are applied to the random forest algorithm, and to the projection pursuit forest, but could be more broadly applied to other bagged ensembles. Interactive graphics are built in R, using the ggplot2, plotly, and shiny packages

Strange Metallic Behavior in Anisotropic Background

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.Comment: 24 pages, 2 figures, minor modification

Derivation of hydrodynamics for the gapless mode in the BEC-BCS crossover from the exact one-loop effective action

We show that many hydrodynamical properties of the BEC/BCS crossover in the presence of a Feshbach resonance at T=0 can be derived easily from the derivative expansion of the (exact) fully renormalized one-loop effective action. In particular, we calculate the velocity of sound throughout the BCS and BEC regimes and derive the generalized superfluid continuity equations for the composite two-fluid system.Comment: Four pages, 1 figure. Whereas v.2 contained additional references, but was otherwise unchanged, this new version contains new material concerning our ability to provide a hydrodynamical description of the BEC/BSC system. This explains the change of title. Our old results are unaffecte