arXiv subjects

C. Wetterich

Publications and source records attributed to C. Wetterich.

At least 91 records · Page 5Linked to original sources

arXiv2009

Probabilistic observables, conditional correlations, and quantum physics

We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The "coarse graining of the information" to micro-states implies probabilistic observables. For two-level probabilistic observables only a probability for finding the values one or minus one can be given for any micro-state, while such observables can be realized as classical observables with sharp values on a substate level. For a continuous family of micro-states parameterized by a sphere all the quantum mechanical laws for a two-state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The non-commutative correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four-state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro-states.

quant-ph↗

arXiv2009

Quantum entanglement and interference from classical statistics

Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical statistical ensemble. Quantum systems are subsystems of larger classical statistical systems, which include the environment or the vacuum. They are characterized by incomplete statistics in the sense that the classical correlation function cannot be used for sequences of measurements in the subsystem.

quant-ph↗

arXiv2009

Exact flow equation for composite operators

We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or "flowing bosonization" of fermionic interactions, or for an effective change of degrees of freedom in dependence on the momentum scale. The flow keeps track of the scale dependent relation between effective composite fields and corresponding composite operators in terms of the fundamental fields.

hep-th↗

arXiv2009

Quantum mechanics from classical statistics

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a "purity constraint". Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

quant-ph↗

arXiv2009

Incommensurate antiferromagnetic fluctuations in the two-dimensional Hubbard model

Commensurate and incommensurate antiferromagnetic fluctuations in the two-dimensional repulsive t-t'-Hubbard model are investigated using functional renormalization group equations. For a sufficient deviation from half filling we establish the existence of local incommensurate order below a pseudocritical temperature T_{pc}. Fluctuations not accounted for in the mean field approximation are important--they lower T_{pc} by a factor \approx2.5.

cond-mat.str-el↗

arXiv2009

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.

cond-mat.stat-mech↗

arXiv2009

Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization

Within the two-dimensional repulsive t-t'-Hubbard model, an attractive coupling in the d-wave pairing channel is induced by antiferromagnetic fluctuations. We investigate this coupling using functional renormalization group equations. The momentum dependent d-wave coupling can be bosonized by the use of scale dependent field transformations. We propose an effective coarse grained model for the Hubbard model which is based on the exchange of antiferromagnetic and d-wave collective bosons.

cond-mat.str-el↗

arXiv2009

Nonperturbative thermodynamics of an interacting Bose gas

We discuss the thermodynamics of a non-relativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependence of pressure, energy and entropy-density, superfluid and condensate-fraction, correlation length, specific heat, isothermal and adiabatic compressibility and various sound velocities. The T->0 limit approaches the quantum phase transition, while the universal critical behavior of a classical second order phase transition in the O(2) universality class determines the region around the critical temperature. Our non-perturbative flow equations based on exact functional renormalization cover all regions in the phase diagram.

cond-mat.quant-gas↗

arXiv2009

Dilatation symmetry in higher dimensions and the vanishing of the cosmological constant

A wide class of dilatation symmetric effective actions in higher dimensions leads to a vanishing four-dimensional cosmological constant. This requires no tuning of parameters and results from the absence of an allowed potential for the scalar dilaton field. The field equations admit many solutions with flat four-dimensional space and non-vanishing gauge couplings. In a more general setting, these are candidates for asymptotic states of cosmological runaway solutions, where dilatation symmetry is realized dynamically if a fixed point is approached as time goes to infinity. Dilatation anomalies during the runaway can lift the degeneracy of solutions and lead to an observable dynamical dark energy.

hep-th↗

arXiv2009

Emergence of quantum mechanics from classical statistics

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables "measure" properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

quant-ph↗

arXiv2009

Superfluid Bose gas in two dimensions

We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe $l$ (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength $λ$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $λ$, and for large $λ$ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature $T_c$ is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density, $T_c/n$, vanishes for $l\to\infty$ logarithmically.

cond-mat.supr-con↗

arXiv2009

Functional renormalization for trion formation in ultracold fermion gases

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $|a|$ the lowest energy state is a "trion" (or trimer) bound state of three atoms. At the location of the resonance, for $|a|\to\infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln |a|$. Extending our findings by continuity to nonzero density and temperature we find that a "trion phase" separates a BEC and a BCS phase, with interesting quantum phase transitions for T=0.

cond-mat.supr-con↗

arXiv2008

Three-body loss in lithium from functional renormalization

We use functional integral methods for an estimate of the three-body loss in a three-component $^6$Li ultracold atom gas. We advocate a simple picture where the loss proceeds by the formation of a three-atom bound state, the trion. In turn, the effective amplitude for the trion formation from three atoms is estimated from a simple effective boson exchange process. The energy gap of the trion and other key quantities for the loss coefficient are computed in a functional renormalization group framework.

cond-mat.other↗

arXiv2008

Particle-hole fluctuations in the BCS-BEC Crossover

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields $T_c/T_F=0.264$. We also investigate the crossover from broad to narrow Feshbach resonances -- for the later we obtain $T_c/T_F=0.204$ for $a^{-1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.

cond-mat.supr-con↗

arXiv2008

Neutrino Lumps in Quintessence Cosmology

Neutrinos interacting with the quintessence field can trigger the accelerated expansion of the Universe. In such models with a growing neutrino mass the homogeneous cosmological solution is often unstable to perturbations. We present static, spherically symmetric solutions of the Einstein equations in the same models. They describe astophysical objects composed of neutrinos, held together by gravity and the attractive force mediated by the quintessence field. We discuss their characteristics as a function of the present neutrino mass. We suggest that these objects are the likely outcome of the growth of cosmological perturbations.

astro-ph↗

arXiv2008

Functional renormalization for Bose-Einstein Condensation

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.

cond-mat.supr-con↗

arXiv2008

Constraints for warped branes

We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution of the field equations. In a higher dimensional world, such constraints arise from variations of the metric which are local in the usual four-dimensional spacetime, without changing the geometry of internal space. As a consequence, continuous families of singular solutions of the field equations, with arbitrary integration constants, are generically reduced to a discrete subset of extrema of the action, similar to regular spaces. As an example, no static extrema of the action with effective four-dimensional gravity exist for six-dimensional gravity with a cosmological constant. These findings explain why the field equations of the reduced four-dimensional theory are not consistent with arbitrary solutions of the higher dimensional field equations - consistency requires the additional constraints. The characteristic solutions for variable tension branes are non-static runaway solutions where the effective four-dimensional cosmological constant vanishes as time goes to infinity.

hep-th↗

arXiv2008

Functional renormalization for quantum phase transitions with non-relativistic bosons

Functional renormalization yields a simple unified description of bosons at zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields. We concentrate on nonrelativistic bosons and an action with a linear time derivative. The ordered phase can be associated with a nonzero density of (quasi) particles $n$. The behavior of observables and correlation functions in the ordered phase depends crucially on the momentum $k_{ph}$, which is characteristic for a given experiment. For the dilute regime $k_{ph}\gtrsim n^{1/d}$ the quantum phase transition is simple, with the same ``mean field'' critical exponents for all $d$ and $M$. On the other hand, the dense regime $k_{ph}\ll n^{1/d}$ reveals a rather rich spectrum of features, depending on $d$ and $M$. In this regime one observes for $d\leq 3$ a crossover to a relativistic action with second time derivatives. This admits order for $d>1$, whereas $d=1$ shows a behavior similar to the low temperature phase of the classical two-dimensional $O(2M)$-models.

cond-mat.supr-con↗