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Chen JP, Teplyaev A, Tsougkas K. Regularized Laplacian determinants of self-similar fractals. LETTERS IN MATHEMATICAL PHYSICS 2017; 108:1563-1579. [PMID: 29755183 PMCID: PMC5932140 DOI: 10.1007/s11005-017-1027-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2017] [Revised: 10/26/2017] [Accepted: 11/01/2017] [Indexed: 06/08/2023]
Abstract
We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of locally self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret their Laplacian determinant as the regularized product of their eigenvalues. We then investigate a connection between the logarithm of the determinant of the discrete graph Laplacian and the regularized one.
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Rodriguez SRK, Casteels W, Storme F, Carlon Zambon N, Sagnes I, Le Gratiet L, Galopin E, Lemaître A, Amo A, Ciuti C, Bloch J. Probing a Dissipative Phase Transition via Dynamical Optical Hysteresis. PHYSICAL REVIEW LETTERS 2017; 118:247402. [PMID: 28665653 DOI: 10.1103/physrevlett.118.247402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Indexed: 06/07/2023]
Abstract
We experimentally explore the dynamical optical hysteresis of a semiconductor microcavity as a function of the sweep time. The hysteresis area exhibits a double power law decay due to the influence of fluctuations, which trigger switching between metastable states. Upon increasing the average photon number and approaching the thermodynamic limit, the double power law evolves into a single power law. This algebraic behavior characterizes a dissipative phase transition. Our findings are in good agreement with theoretical predictions for a single mode resonator influenced by quantum fluctuations, and the present experimental approach is promising for exploring critical phenomena in photonic lattices.
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Affiliation(s)
- S R K Rodriguez
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - W Casteels
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, Sorbonne Paris Cité and CNRS, UMR 7162, 75205 Paris Cedex 13, France
| | - F Storme
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, Sorbonne Paris Cité and CNRS, UMR 7162, 75205 Paris Cedex 13, France
| | - N Carlon Zambon
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - I Sagnes
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - L Le Gratiet
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - E Galopin
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - A Amo
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - C Ciuti
- Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, Sorbonne Paris Cité and CNRS, UMR 7162, 75205 Paris Cedex 13, France
| | - J Bloch
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
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Dedovich T, Tokarev M. Analysis of fractal events with background. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201713807009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tanese D, Gurevich E, Baboux F, Jacqmin T, Lemaître A, Galopin E, Sagnes I, Amo A, Bloch J, Akkermans E. Fractal energy spectrum of a polariton gas in a Fibonacci quasiperiodic potential. PHYSICAL REVIEW LETTERS 2014; 112:146404. [PMID: 24765996 DOI: 10.1103/physrevlett.112.146404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2013] [Indexed: 06/03/2023]
Abstract
We report on the study of a polariton gas confined in a quasiperiodic one-dimensional cavity, described by a Fibonacci sequence. Imaging the polariton modes both in real and reciprocal space, we observe features characteristic of their fractal energy spectrum such as the opening of minigaps obeying the gap labeling theorem and log-periodic oscillations of the integrated density of states. These observations are accurately reproduced solving an effective 1D Schrödinger equation, illustrating the potential of cavity polaritons as a quantum simulator in complex topological geometries.
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Affiliation(s)
- D Tanese
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - E Gurevich
- Department of Physics, Technion Israel Institute of Technology, Haifa 32000, Israel
| | - F Baboux
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - T Jacqmin
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - A Lemaître
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - E Galopin
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - I Sagnes
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - A Amo
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - J Bloch
- Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - E Akkermans
- Department of Physics, Technion Israel Institute of Technology, Haifa 32000, Israel
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Laiho J, Coumbe D. Evidence for asymptotic safety from lattice quantum gravity. PHYSICAL REVIEW LETTERS 2011; 107:161301. [PMID: 22107374 DOI: 10.1103/physrevlett.107.161301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2011] [Indexed: 05/31/2023]
Abstract
We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ∼3/2 at short distance to ∼4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.
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Affiliation(s)
- J Laiho
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
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