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We study fermions at quantum criticality with extremely retarded interactions of the form $V(\omega_l)=(g/|\omega_l|)^\gamma$, where $\omega_l$ is the transferred Matsubara frequency. This system undergoes a normal-superconductor phase transition at a critical temperature $T=T_c$. The order parameter is the frequency-dependent gap function $\Delta(\omega_n)$ as in the Eliashberg theory. In general, the interaction is extremely retarded for $\gamma\gg 1$, except at low temperatures $\gamma>3$ is sufficient. We evaluate the normal state specific heat, $T_c$, the jump in the specific heat, $\Delta(\omega_n)$ near $T_c$, and the Landau free energy. Our answers are asymptotically exact in the limit $\gamma\to\infty$. At low temperatures, we prove that the global minimum of the free energy is nondegenerate and determine the order parameter, the free energy, and the specific heat. These answers are exact for $T\to0$ and $\gamma>3$. We also uncover and investigate an instability of the $\gamma$ model: negative specific heat at $T\to0$ and just above $T_c$., Comment: 15 pages, 4 figures, 1 table, refs updated & text polished

This paper studies a model with multifractal wave functions and fractal mini-bands which allows for analytical derivation of its phase diagram

Attempts to resolve the long-standing Fermion mass hierarchy problem in frames of the AdS/CFT correspondence demand the knowledge of bulk fermion masses. The approach of the “old” conformal bootstrap in the anti-de Sitter (AdS) context permitted calculating bulk masses of scalar fields, as it was shown in three previous papers B. L. Altshuler [arXiv:1810.01105; Int. J. Mod. Phys. 2050001 (2020)10.1142/S0217751X20500013; J. High Energy Phys. 01 (2020) 13710.1007/JHEP01(2020)137]. In the present paper, this approach is extended to physically more interesting spin-1/2 bulk fields. Calculation of spinor-scalar vertices is performed in physical AdS space, and unexpectedly simple expressions for spinor-scalar bubbles (two-point one-loop self-energy Witten diagrams) are obtained. The “double-trace from UV to IR flow” subtraction of UV divergences used earlier in calculations of the UV-finite bulk tadpoles is applied to bubbles. This permitted us to write down in the frame of the old conformal bootstrap approach the nontrivial spectral equations for the bulk fermion masses; the SU(N) Yukawa model of spinor fields interacting with conformal invariant scalar field in case of four boundary dimensions is considered as a specific example.

We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population of the cavity photons. Even though the dynamics of each ensemble are chaotic, their motions repeat one another. In our system, chaos first emerges via quasiperiodicity and then synchronizes. We identify the signatures of synchronized chaos, chaos, and quasiperiodicity in the experimentally observable power spectra of the light emitted by the cavity., 8 pages, 9 figures, published version

The surprising simplicity of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants permits to obtain compact expressions for UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary conditions. This result generalizes Gubser and Mitra calculation for particular case of difference of "regular" and "irregular" one-loop energies in one-brane RS-model. Approach developed in the paper also allows to get "in one line" the one-loop quantum energies in two-brane RS-model. The relationship between "one-loop" expressions corresponding to mixed Robin and to double-trace asymptotic boundary conditions is traced., Comment: 16 pages

The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the individual qubits and quantum gates. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources obtained by clever engineering. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, quantum devices are affected by noise decreasing with frequency, f, approximately as 1/f. According to the present point of view, such noise is due to material- and device-specific microscopic degrees of freedom interacting with quantum variables of the nanodevice. The simplest picture is that the environment that destroys the phase coherence of the device can be thought of as a system of two-state fluctuators, which experience random hops between their states. If the hopping times are distributed in a exponentially broad domain, the resulting fluctuations have a spectrum close to 1/f in a large frequency range. In this paper we review the current state of the theory of decoherence due to degrees of freedom producing 1/f noise. We discuss basic mechanisms of such noises in various nanodevices and then review several models describing the interaction of the noise sources with quantum devices. The main focus of the review is to analyze how the 1/f noise destroys their coherent operation. We start from individual qubits concentrating mostly on the devices based on superconductor circuits, and then discuss some special issues related to more complicated architectures. Finally, we consider several strategies for minimizing the noise-induced decoherence.

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(\alpha)$ defined in Eq.(3), remains positive for $\alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated., Comment: 5 pages, 3 figures + 4 pages supplemental material. arXiv admin note: text overlap with arXiv:1401.0019

This paper is devoted to the magnetic properties of isolated mesoscopic grains. We demonstrate that under very general conditions the electron-electron interactions in such grains can be taken into account by a simple interaction Hamiltonian. This Hamiltonian involves only three coupling constants, which correspond to charging, exchange interaction, and superconducting correlations. The most important condition for such a description is that Thouless conductance of each grain is large. Under this condition sample-to-sample fluctuations of the coupling constants can be neglected. However, the thermodynamic properties can still remain sample specific due to the one-electron part of the Hamiltonian. If the grain is made from a material that is close to the threshold of ferromagnetic instability, the mesoscopic fluctuations of the magnetization are especially strong. Moreover, the situation becomes multistable: free energy of each grain as a function of the magnetization is characterized by a large number of local minima. We analyze the statistics of these minima and show that it possesses simple scaling properties. Numerical simulations confirm this scaling.

We consider the adiabatic charge transport through zero-dimensional mesoscopic sample (quantum dot) caused by two periodically changing external perturbations. Both the magnitude and the sign of the transmitted charge are extremely sensitive to the configuration of the dot and to the magnetic field. We find the correlation function characterizing the random value of this pumped charge for arbitrary strength of the perturbation. In contrast to previous theoretical and experimental claims, the charge is found not to have any symmetry with respect to the inversion of magnetic field. At strong pumping perturbation, the variance of the charge $$ is found to be proportional to the length of the contour in parametric space., Comment: 11 pages, 5 figures included

It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the oxide layer. The gate voltage changes the number of charged traps which results in a sharp change in the resistivity. The observed exponential temperature dependence of the resistivity in the metallic phase of the transition follows from the temperature dependence of the trap occupation number. The model naturally describes the experimentally observed scaling properties of the transition and effects of magnetic and electric fields.

This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds to the infinite conductance of the grains, these moments are self-averaging quantities. At large but finite conductance the moments do fluctuate due to the long range correlations in the eigenfunctions. We evaluate the distributions of fluctuations at given conductance and geometry of the grains and express them through the spectrum of the diffusion operator in the grain., Comment: RevTeX, 4 pages, no figure

The problem of electron--electron lifetime in a quantum dot is studied beyond perturbation theory by mapping it onto the problem of localization in the Fock space. We identify two regimes, localized and delocalized, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are very close to single particle excitations. In the delocalized state, each eigenstate is a superposition of states with very different quasiparticle content. A transition between the two regimes occurs at the energy $\simeq\Delta(g/\ln g)^{1/2}$, where $\Delta$ is the one particle level spacing, and $g$ is the dimensionless conductance. Near this energy there is a broad critical region in which the states are multifractal, and are not described by the Golden Rule., Comment: 13 pages, LaTeX, one figure

We explain the observation of clusters in the tunneling resonance spectra of small metallic particles of few nanometer size. Each cluster of resonances is identified with one excited single--electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single--electron states. Assuming the underlying classical dynamics of the electrons to be chaotic, we determine the typical shift to be $\Delta/g$ where $g$ is the dimensionless conductance of the grain., Comment: 4 pages, 2 .eps figures enclosed

We study the effect of electron-electron (e-e) interactions on compressibility, capacitance and inverse compressibility of electrons in a quantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged compressibility and capacitance decreases as a function of the interaction strength, while the mean inverse compressibility increases. Fluctuations of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compressibility also turn out to be much smaller than their averages. The analytical calculations are compared with the results of a numerical calculation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak interaction values is found. Implications for the interpretation of current experimental data are discussed., REVTeX, 23 pages, 6 figures, accepted for publication in PRB

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive., 9 pages, Revtex, with eps figures,to appear in Phys Rev B

We analyze pairing in two dimensional spin liquids. We argue that interplane pairing enhanced by magnetic correlations is the most plausible explanation of the spin gap phenomenon observed in underdoped cuprates. The details of the pairing theory depend on the in-plane antiferromagnetic correlations. We consider two models: $2p_F$ correlations induced by a strong gauge field interaction and undamped spin waves. We estimate the pairing temperature $T_s$ and the angular dependence of the gap function and discuss physical consequences., Comment: 1 pages, 2 Postscript figures in a separate file

We study T=0 spin-density-wave transitions in two-dimensional Fermi liquids in which the ordering wave vector Q is such that the tangents to the Fermi line at the points connected by Q are parallel (e.g., Q=2${\mathit{p}}_{\mathit{F}}$ in a system with a circular Fermi line) and the Fermi line is not flat. We show that the transition is first order if the ordering wave vector Q is not commensurate with a reciprocal lattice vector G, i.e., Q\ensuremath{\ne}G/2. If Q is close to G/2 the transition is weakly first order and an intermediate scaling regime exists; in this regime the 2${\mathit{p}}_{\mathit{F}}$ susceptibility and observables such as the NMR rates ${\mathit{T}}_{1}$ and ${\mathit{T}}_{2}$ have scaling forms which we determine.

Bi-tensor kernel in integral form of Einstein equations realizing Mach's idea of non-existence of empty space-times is taken as an inverse of differential operator ("Mach operator") defined conventionally as a second variation of Einstein's gravity Action over contravariant components of metric tensor. The choice of transverse gauge condition used in this definition does not influence results of the paper since only transverse and traceless tensor modes written on different background space-times are studied. Presence of ghosts among modes of Mach operator invalidates the integral formulation of Einstein equations. And the demand of absence of these ghosts proves to be a selection rule for dimensionality of the background space-time. In particular Mach operator written on De Sitter background or on the background of so called "Einstein Universe" does not possess tensor ghosts only in 4-dimensions. The similar demand gives non-trivial formula for dimensionalities of subspaces of the Freund-Rubin background.

In spite of having finite life-time exciton-polaritons in microcavities are known to condense at strong enough pumping of the reservoir. We present an analytical theory of such Bose-condensates on a set of localized one-particle states: condensation centers. To understand physics of these arrays one has to supplement the Josephson coupling by the radiative coupling caused by the interference of the light emitted by different centers. Combination of these couplings with the one-site interaction between the bosons leads to a rich nonlinear dynamics. In particular, a new regime of radiation appears. We call it weak lasing: the centers have macroscopic occupations and radiate coherently, but the coupling alone is sufficient for stabilization. The system can have several stable states and switch between them. Moreover, the time reversal symmetry in this regime is, as a rule, broken. A number of existing experimental puzzles find natural interpretation in the framework of this theory., 5 pages, 2 figures

The response of the many-particle spectrum of a system of strongly correlated particles to arbitrary perturbations is shown to display the same universality as that derived for the single-particle properties of weakly disordered metals'and recently shown to apply to numerous quantum chaotic systems

We study a quantum quench in a 1D system possessing Luttinger liquid (LL) and Mott insulating ground states before and after the quench, respectively. We show that the quench induces power law amplification in time of any particle density inhomogeneity in the initial LL ground state. The scaling exponent is set by the fractionalization of the LL quasiparticle number relative to the insulator. As an illustration, we consider the traveling density waves launched from an initial localized density bump. While these waves exhibit a particular rigid shape, their amplitudes grow without bound.

We show that a dilute ensemble of epoxy-bonded adatoms on graphene has a tendency to form a spatially correlated state accompanied by a gap in graphene's electron spectrum. This effect emerges from the electron-mediated interaction between adatoms with a peculiar $1/r^3$ distance dependence. The partial ordering transition is described by a random bond three state Potts model., 4 pages, 2 figures

The magnetoconductance in YBa2Cu3O7-delta grain boundary Josephson junctions displays fluctuations at low temperatures of mesoscopic origin. The morphology of the junction suggests that transport occurs in narrow channels across the grain boundary line with a large Thouless energy. Nevertheless the measured fluctuation amplitude decreases quite slowly when increasing the voltage up to values about 20 times the Thouless energy, of the order of the nominal superconducting gap. Our findings show the coexistence of supercurrent and quasiparticle current in the junction conduction even at high nonequilibrium conditions. Model calculations confirm the reduced role of quasiparticle relaxation at temperatures up to 3 K.

Bilayer graphene (two coupled graphitic monolayers arranged according to Bernal stacking) is a two-dimensional gapless semiconductor with a peculiar electronic spectrum different from the Dirac spectrum in the monolayer material. In particular, the electronic Fermi line in each of its valleys has a strong p -> -p asymmetry due to a trigonal warping, which suppresses the weak localization effect. We show that weak localisation in bilayer graphene may be present only in devices with pronounced intervalley scattering, and we evaluate the corresponding magnetoresistance., 4 pages, 1 figure

Magnetofluctuations of the normal-state resistance R-N have been reproducibly observed in high-critical-temperature superconductor (HTS) grain boundary junctions at low temperatures. We attribute them to mesoscopic transport in narrow channels across the grain boundary line. The Thouless energy appears to be the relevant energy scale. Our findings have significant implications for quasiparticle relaxation and coherent transport in HTS grain boundaries.

The decoherence of a qubit due to a classical non-Gaussian noise with correlation time longer than the decoherence time is discussed for arbitrary working points of the qubit. A method is developed that allows an exact formula for the phase memory functional in the presence of independent random telegraph noise sources to be derived., Comment: 12 pages, 7 figures

We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. We demonstrate that possible initial states of the condensate fall into two classes. In the first case, the order parameter asymptotes to a constant value. The approach to a constant is oscillatory with an inverse square root decay. This happens, e.g., when the strength of pairing is abruptly changed while the system is in the paired ground state and more generally for any nonequilibrium state that is in the same class as the ground state. In the second case, the order parameter exhibits persistent oscillations with several frequencies. This is realized for nonequilibrium states that belong to the same class as excited stationary states. Our classification of initial states extends the concept of excitation spectrum to nonequilibrium regime and allows one to predict the evolution without solving equations of motion.

We study decoherence in a qubit with the distance between the two levels affected by random flips of bistable fluctuators. For the case of a single fluctuator we evaluate explicitly an exact expression for the phase-memory decay in the echo experiment with a resonant ac excitation. The echo signal as a function of time shows a sequence of plateaus. The position and the height of the plateaus can be used to extract the fluctuator switching rate \gamma and its coupling strength v. At small times the logarithm of the echo signal is proportional to t^3. The plateaus disappear when the decoherence is induced by many fluctuators. In this case the echo signal depends on the distribution of the fluctuators parameters. According to our analysis, the results significantly deviate from those obtained in the Gaussian model as soon as v greater than \gamma., Comment: 4 pages, 2 figures

We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. Possible initial states of the condensate fall into two classes. In the first case, the order parameter asymptotes to a constant value. The approach to a constant is oscillatory with an inverse square root decay. This happens, e.g., when the strength of pairing is abruptly changed while the system is in the paired ground state and more generally for any nonequilibrium state that is in the same class as the ground state. In the second case, the order parameter exhibits persistent oscillations with several frequencies. This is realized for nonequilibrium states that belong to the same class as excited stationary states.

A theoretical interpretation of the recent experiments of Astafiev et. al. on the T_1-relaxation rate in Josephson Charge Qubits is proposed. The experimentally observed reproducible nonmonotonic dependence of T_1 on the splitting E_J of the qubit levels suggests further specification of the previously proposed models of the background charge noise. From our point of view the most promising is the ``Andreev fluctuator'' model of the noise. In this model the fluctuator is a Cooper pair that tunnels from a superconductor and occupies a pair of localized electronic states. Within this model one can naturally explain both the average linear T_1(E_J) dependence and the irregular fluctuations. The role of fluctuators in the formation of strong resonant peaks in this dependence is also discussed., Comment: 4 pages, 3 figures

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies., Comment: 22 pages, 1 figure

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting two-dimensional electron gas (2DEG). We include the effect of the Fermi-liquid background by solving the two-dimensional (2D) Bethe-Salpeter equation for the two-particle Green function vertex in the ladder and random phase approximations. This result is used to discuss the feasibility of producing spin-EPR pairs in a 2DEG by collecting electrons emerging from collisions at a $\ensuremath{\pi}∕2$ scattering angle, where only the entangled spin singlets avoid the destructive interference resulting from quantum indistinguishability. Furthermore, we study the effective 2D electron-electron interaction due to the exchange of virtual acoustic and optical phonons and compare it to the Coulomb interaction. Finally, we show that the 2D Kohn-Luttinger pairing instability for the scattering electrons is negligible in a GaAs 2DEG.

The paper is devoted to the study of the effects due to superconducting pairing in small metallic grains. We explicitly determine the low-energy spectrum of the problem at strong superconducting coupling and in the limit of large Thouless conductance. We start with the strong-coupling limit and develop a systematic expansion in powers of the inverse coupling constant for the many-particle spectrum of the system. The strong- coupling expansion is based on the formal exact solution of the Richardson model and converges for realistic values of the coupling constant. We use this expansion to study the low-energy excitations of the system, in particular energy and spin gaps in the many-body spectrum.

We study the energy distribution function of quasiparticles in short voltage biased mesoscopic wires in the presence of magnetic impurities and applied magnetic field. The system is described by a Boltzmann equation where the collision integral is determined by coupling to spin-$\frac{1}{2}$ impurities. We develop a theory of the coupling of nonequilibrium electrons to dissipative spins. This theory is valid as long as the characteristic smearing of the steps in the energy distribution function, which depends both on the bias voltage and the location of the probe, exceeds the Kondo temperature. We further address the renormalization of coupling constants by nonequilibrium electrons. Magnetic-field dependence of the energy relaxation rate turns out to be nonmonotonic. For low magnetic field an enhancement of energy relaxation is found, whereas for larger magnetic fields the energy relaxation decreases again meeting qualitatively the experimental findings by Anthore et al. (cond-mat/0109297). This gives a strong indication that magnetic impurities are in fact responsible for the enhanced energy relaxation in copper wires. Our theoretical results are in good agreement with the experiment at large bias voltages where the theory is applicable. At the same time, at small bias voltages there are substantial quantitative deviations. Furthermore, the concentration of the spins, which follows from the energy relaxation for Cu, seems to to be substantially higher than the concentration estimated from weak localization (dephasing rate) measurements. Since the approach presented is valid only above Kondo temperature, it does not apply to the related problem of weak localization at low temperature in equilibrium.

Physics Department, Princeton University, Princeton, New Jersey 08544and NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540~Received 4 March 2002; published 29 July 2002!Within random matrix theory for quantum dots, both the dot’s one-particle eigenlevels and the dot-leadcouplings are statistically distributed. While the effect of the latter on the conductance is obvious and has beentaken into account in the literature, the statistical distribution of the one-particle eigenlevels is generallyreplaced by a picket-fence spectrum. Here we take the random matrix theory eigenlevel distribution explicitlyinto account, and observe significant deviations in the conductance distribution and magnetoconductance ofclosed quantum dots at experimentally relevant temperatures.DOI: 10.1103/PhysRevB.66.033308 PACS number~s!: 73.23.Ad

In the limit of weak exchange, J, at low hole concentration, the ground state of the 2D t-J model is believed to be ferromagnetic. We study the leading instability of this Nagaoka state, which emerges with increasing J. Both exact diagonalization of small clusters, and a semiclassical analytical calculation of larger systems show that above a certain critical value of the exchange, Nagaoka's state is unstable to phase separation. In a finite-size system a bubble of antiferromagnetic Mott insulator appears in the ground state above this threshold. The size of this bubble depends on the hole concentration and scales as a power of the system size, N.

Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and the master equation. The combination of this analysis with recent experiments on the magnetoconductance allows, for the first time, the evaluation of the dephasing times of closed quantum dots. These dephasing times turn out to be dependent on the mean level spacing and significantly enhanced as compared with the case of open dots. Moreover, the experimental data available are consistent with the prediction that the dephasing of one-particle states in finite closed systems disappears at low enough energies and temperatures.

We study the Anderson orthogonality catastrophe (AOC) in finite conductors with diffusive disorder. The disorder averaged logarithm of $\chi$, the overlap between the ground states before and after adding a static impurity, is found to depend nonmonotonically on the disorder. In two dimensions $ \propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence on the number of electrons $N$ than in the canonical AOC. A very broad tail of the distribution of $\chi$, found numerically, is a signature of the importance of a few-level statistics at the Fermi energy., Comment: 4 pages, 3 figures

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of single-parameter scaling in this model. According to this criterion, states with energies within the conduction band of the underlying nonrandom system satisfy single-parameter scaling when the disorder is small enough. At the same time, single-parameter scaling is not valid for states close to band boundaries and those outside of the original spectrum, even in the case of small disorder. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $\ensuremath{\delta}$ functions with random strengths. We show that an increase in disorder can restore single-parameter scaling behavior for states within the band gaps.

A Comment of the Letter by D. C. Ralph et al., Phys. Rev. Lett. 72, 1064 (1994). The authors of the Letter offer a Reply.

Interaction effects in disordered Fermi systems are considered in the metallic regime. In two dimensions, logarithmic corrections are obtained for conductivity, density of states, specific heat, and Hall constant. These results are compared with a recent theory of localization as well as some experiments.