Many-body physics and quantum chaos

Ullmo, Denis

doi:10.1088/0034-4885/71/2/026001

Cited by 45 publications

(55 citation statements)

References 246 publications

(471 reference statements)

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“…In fact, the generalization of the van Vleck-Gutzwiller propagator to describe systems of interacting particles does not pose any conceptual challenge, as the classical limit of the theory is very well understood. The semiclassical propagator is now an established tool to describe quantum dynamics of molecular systems [13,14,15,16] and mesoscopic electronic systems [17].…”

Section: Introductionmentioning

confidence: 99%

The semiclassical propagator in fermionic Fock space

et al. 2014

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We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form D[ψ, ψ * ]e iR[ψ,ψ * ] with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space.As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.

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Section: Introductionmentioning

confidence: 99%

The semiclassical propagator in fermionic Fock space

et al. 2014

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“…This issue has been studied but only for nonrelativistic quantum systems [66][67][68][69]. We address this problem in relativistic quantum mechanics using graphene systems in the setting of resonant tunneling, where the electron-electron Coulomb interactions are described by the mean-field Hubbard Hamiltonian.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…However, in these works on quantum chaos, the standard setting was that of single-particle quantum dynamics, whereas many-body effects such as electron-electron interactions were ignored. While there were also previous studies of the interplay between many-body interactions and classical chaos [66][67][68][69], these were exclusively for nonrelativistic quantum systems described by the Schrödinger equation. To investigate the effect of chaos on relativistic quantum systems with manybody interactions has thus been an outstanding problem, yet it is not only fundamental to physics, but also important for the practical development of relativistic quantum devices.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaotic tunneling in graphene systems with electron-electron interactions

et al. 2014

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An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

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“…In the high-temperature regime T ≥ T 0 K such universality follows from a perturbative renormalization argument (although not so straightforwardly, see the discussion in refs [4,25]). Furthermore, comparison with quantum Monte Carlo results shows that predictions obtained in this way are quantitatively very accurate [4,5].…”

Section: The T Regimementioning

confidence: 99%

Kondo effect and mesoscopic fluctuations

et al. 2011

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International audienceTwo important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature TK which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/TK. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling

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Many-body physics and quantum chaos

Cited by 45 publications

References 246 publications

The semiclassical propagator in fermionic Fock space

The semiclassical propagator in fermionic Fock space

Quantum chaotic tunneling in graphene systems with electron-electron interactions

Kondo effect and mesoscopic fluctuations

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