219 results on '"P. Le Doussal"'
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2. A New TGF-β Mimetic, XEP™-716 Miniprotein™, Exhibiting Regenerative Properties Objectivized by Instrumental Evaluation
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Chajra, Hanane, Saguet, Thibaut, Granger, Corinne, Breton, Lionel, Pinto, Pedro Contreiras, Machicoane, Mickael, and Le Doussal, Jean Marc
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- 2024
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3. Correction: A New TGF-β Mimetic, XEP™-716 Miniprotein™, Exhibiting Regenerative Properties Objectivized by Instrumental Evaluation
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Chajra, Hanane, Saguet, Thibaut, Granger, Corinne, Breton, Lionel, Pinto, Pedro Contreiras, Machicoane, Mickael, and Le Doussal, Jean Marc
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- 2024
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4. A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems
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Federico Gerbino, Pierre Le Doussal, Guido Giachetti, and Andrea De Luca
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random matrix theory ,monitored quantum systems ,measurement-induced phase transitions ,Physics ,QC1-999 - Abstract
We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.
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- 2024
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5. Replica-Symmetry Breaking Transitions in the Large Deviations of the Ground-State of a Spherical Spin-Glass
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Lacroix-A-Chez-Toine, Bertrand, Fyodorov, Yan V., and Le Doussal, Pierre
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- 2024
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6. Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions
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Pierre Le Doussal, Naftali R. Smith, Nathan Argaman
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Physics ,QC1-999 - Abstract
We consider a system of $N$ spinless fermions, interacting with each other via a power-law interaction $\epsilon/r^n$, and trapped in an external harmonic potential $V(r) = r^2/2$, in $d=1,2,3$ dimensions. For any $0 < n < d+2$, we obtain the ground-state energy $E_N$ of the system perturbatively in $\epsilon$, $E_{N}=E_{N}^{≤ft(0)}+\epsilon E_{N}^{≤ft(1)}+O≤ft(\epsilon^{2})$. We calculate $E_{N}^{≤ft(1)}$ exactly, assuming that $N$ is such that the "outer shell" is filled. For the case of $n=1$ (corresponding to a Coulomb interaction for $d=3$), we extract the $N \gg 1$ behavior of $E_{N}^{≤ft(1)}$, focusing on the corrections to the exchange term with respect to the leading-order term that is predicted from the local density approximation applied to the Thomas-Fermi approximate density distribution. The leading correction contains a logarithmic divergence, and is of particular importance in the context of density functional theory. We also study the effect of the interactions on the fermions' spatial density. Finally, we find that our result for $E_{N}^{≤ft(1)}$ significantly simplifies in the case where $n$ is even.
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- 2024
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7. Universal Out-of-Equilibrium Dynamics of 1D Critical Quantum Systems Perturbed by Noise Coupled to Energy
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Alexios Christopoulos, Pierre Le Doussal, Denis Bernard, and Andrea De Luca
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Physics ,QC1-999 - Abstract
We consider critical one-dimensional quantum systems initially prepared in their ground state and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any two-point chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast to the general expectation of heating, we demonstrate that, over the noise realizations, the system reaches a nontrivial and universal stationary distribution of states characterized by broad tails of physical quantities. As an example, we analyze the entanglement entropy production associated to a given interval of size ℓ. The corresponding stationary distribution has a 3/2 right tail for all ℓ and converges to a one-sided Levy stable for large ℓ. We obtain a similar result for the local energy density: While its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with 3/2 decay exponent. We show that this stationary distribution for the energy density emerges even if the initial state is prepared at finite temperature. Our results are benchmarked via analytical and numerical calculations for a chain of noninteracting spinless fermions with excellent agreement.
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- 2023
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8. Half-Space Stationary Kardar–Parisi–Zhang Equation
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Barraquand, Guillaume, Krajenbrink, Alexandre, and Le Doussal, Pierre
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- 2020
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9. Manifolds Pinned by a High-Dimensional Random Landscape: Hessian at the Global Energy Minimum
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Fyodorov, Yan V. and Le Doussal, Pierre
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- 2020
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10. Non-crossing Brownian Paths and Dyson Brownian Motion Under a Moving Boundary
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Gautié, Tristan, Le Doussal, Pierre, Majumdar, Satya N., and Schehr, Grégory
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- 2019
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11. Spherical Spin Glass Model with External Field
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Baik, Jinho, Collins-Woodfin, Elizabeth, Le Doussal, Pierre, and Wu, Hao
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- 2021
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12. Systematic time expansion for the Kardar–Parisi–Zhang equation, linear statistics of the GUE at the edge and trapped fermions
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Alexandre Krajenbrink, Pierre Le Doussal, and Sylvain Prolhac
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Nuclear and particle physics. Atomic energy. Radioactivity ,QC770-798 - Abstract
We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the long time large deviation function, found to agree with previous works using completely different techniques. Unexpected similarities with stationary large deviations of TASEP with periodic and open boundaries are discussed. Two additional applications are given. (i) Our method is generalized to study the linear statistics of the Airy point process, i.e. of the GUE edge eigenvalues. We obtain the generating function of the cumulants of the empirical measure to a high order. The second cumulant is found to match the result in the bulk obtained from the Gaussian free field by Borodin and Ferrari [1,2], but we obtain systematic corrections to the Gaussian free field (higher cumulants, expansion towards the edge). This also extends a result of Basor and Widom [3] to a much higher order. We obtain large deviation functions for the Airy point process for a variety of linear statistics test functions. (ii) We obtain results for the counting statistics of trapped fermions at the edge of the Fermi gas in both the high and the low temperature limits.
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- 2018
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13. Distribution of Brownian Coincidences
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Krajenbrink, Alexandre, Lacroix-A-Chez-Toine, Bertrand, and Le Doussal, Pierre
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- 2019
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14. Identification of 9-O-acetyl-N-acetylneuraminic acid (Neu5,9Ac2) as main O-acetylated sialic acid species of GD2 in breast cancer cells
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Cavdarli, Sumeyye, Dewald, Justine H., Yamakawa, Nao, Guérardel, Yann, Terme, Mickaël, Le Doussal, Jean-Marc, Delannoy, Philippe, and Groux-Degroote, Sophie
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- 2019
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15. Field theory of disordered elastic interfaces at 3-loop order: The β-function
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Kay Jörg Wiese, Christoph Husemann, and Pierre Le Doussal
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Nuclear and particle physics. Atomic energy. Radioactivity ,QC770-798 - Abstract
We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group β-function to third order in ε=4−d, in an expansion in the dimension d around the upper critical dimension d=4. The calculations are performed using exact RG, and several other techniques, which allow us to resolve consistently the problems associated with the cusp of the renormalized disorder.
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- 2018
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16. Full counting statistics for interacting trapped fermions
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Naftali R. Smith, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr
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Physics ,QC1-999 - Abstract
We study $N$ spinless fermions in their ground state confined by an external potential in one dimension with long range interactions of the general Calogero-Sutherland type. For some choices of the potential this system maps to standard random matrix ensembles for general values of the Dyson index $\beta$. In the fermion model $\beta$ controls the strength of the interaction, $\beta=2$ corresponding to the noninteracting case. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the Fermi gas. We predict that for general $\beta$ the variance of ${\cal N}_{\cal D}$ grows as $A_{\beta} \log N + B_{\beta}$ for $N \gg 1$ and we obtain a formula for $A_\beta$ and $B_\beta$. This is based on an explicit calculation for $\beta\in\left\{ 1,2,4\right\} $ and on a conjecture that we formulate for general $\beta$. This conjecture further allows us to obtain a universal formula for the higher cumulants of ${\cal N}_{\cal D}$. Our results for the variance in the microscopic regime are found to be consistent with the predictions of the Luttinger liquid theory with parameter $K = 2/\beta$, and allow to go beyond. In addition we present families of interacting fermion models in one dimension which, in their ground states, can be mapped onto random matrix models. We obtain the mean fermion density for these models for general interaction parameter $\beta$. In some cases the fermion density exhibits interesting transitions, for example we obtain a noninteracting fermion formulation of the Gross-Witten-Wadia model.
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- 2021
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17. Role of Sialyl-O-Acetyltransferase CASD1 on GD2 Ganglioside O-Acetylation in Breast Cancer Cells
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Sumeyye Cavdarli, Larissa Schröter, Malena Albers, Anna-Maria Baumann, Dorothée Vicogne, Jean-Marc Le Doussal, Martina Mühlenhoff, Philippe Delannoy, and Sophie Groux-Degroote
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ganglioside ,sialic acid ,O-acetylation ,CASD1 ,OAcGD2 ,breast cancer ,Cytology ,QH573-671 - Abstract
The O-acetylated form of GD2, almost exclusively expressed in cancerous tissues, is considered to be a promising therapeutic target for neuroectoderm-derived tumors, especially for breast cancer. Our recent data have shown that 9-O-acetylated GD2 (9-OAcGD2) is the major O-acetylated ganglioside species in breast cancer cells. In 2015, Baumann et al. proposed that Cas 1 domain containing 1 (CASD1), which is the only known human sialyl-O-acetyltransferase, plays a role in GD3 O-acetylation. However, the mechanisms of ganglioside O-acetylation remain poorly understood. The aim of this study was to determine the involvement of CASD1 in GD2 O-acetylation in breast cancer. The role of CASD1 in OAcGD2 synthesis was first demonstrated using wild type CHO and CHOΔCasd1 cells as cellular models. Overexpression using plasmid transfection and siRNA strategies was used to modulate CASD1 expression in SUM159PT breast cancer cell line. Our results showed that OAcGD2 expression was reduced in SUM159PT that was transiently depleted for CASD1 expression. Additionally, OAcGD2 expression was increased in SUM159PT cells transiently overexpressing CASD1. The modulation of CASD1 expression using transient transfection strategies provided interesting insights into the role of CASD1 in OAcGD2 and OAcGD3 biosynthesis, and it highlights the importance of further studies on O-acetylation mechanisms.
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- 2021
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18. Antenatal magnesium sulphate administration for fetal neuroprotection: a French national survey
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Clément Chollat, Lise Le Doussal, Gaëlle de la Villéon, Delphine Provost, and Stéphane Marret
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Magnesium sulphate ,Neuroprotection ,Neonatology ,Very preterm infants ,National survey ,Gynecology and obstetrics ,RG1-991 - Abstract
Abstract Background Magnesium sulphate (MgSO4) is the only treatment approved for fetal neuroprotection. No information on its use is available in the absence of a national registry of neonatal practices. The objective of our study was to evaluate the use of MgSO4 for fetal neuroprotection in French tertiary maternity hospitals (FTMH). Methods Online and phone survey of all FTMH between August 2014 and May 2015. A participation was expected from one senior obstetrician, one senior anaesthetist and one senior neonatologist from each FTMH. Information was obtained from 63/63 (100%) FTMH and 138/189 (73%) physicians. Use of MgSO4 for fetal neuroprotection, regimen and injection protocols, reasons for non-use were the main outcome measures. Results 60.3% of FTMH used MgSO4 for fetal neuroprotection. No significant difference was observed between university and non-university hospitals or according to the annual number of births. Protocols differed especially in terms of the maximum gestational age (3%
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- 2017
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19. Impurities in systems of noninteracting trapped fermions
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David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr
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Physics ,QC1-999 - Abstract
We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-P\'ech\'e (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.
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- 2021
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20. Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
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Alexandre Krajenbrink, Pierre Le Doussal
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Physics ,QC1-999 - Abstract
We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A - \frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= \frac{1}{2}$, the critical point at which the DP binds to the wall, we obtain the GOE Tracy-Widom distribution. In the critical region, $A+\frac{1}{2} = \epsilon t^{-1/3} \to 0$ with fixed $\epsilon = \mathcal{O}(1)$, we obtain a transition kernel continuously depending on $\epsilon$. Our work extends the results obtained previously for $A=+\infty$, $A=0$ and $A=- \frac{1}{2}$.
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- 2020
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21. Profiling of O-acetylated Gangliosides Expressed in Neuroectoderm Derived Cells
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Sumeyye Cavdarli, Nao Yamakawa, Charlotte Clarisse, Kazuhiro Aoki, Guillaume Brysbaert, Jean-Marc Le Doussal, Philippe Delannoy, Yann Guérardel, and Sophie Groux-Degroote
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gangliosides ,o-acetylation ,mass spectrometry ,neuroectoderm-derived cancer ,sialic acid ,Biology (General) ,QH301-705.5 ,Chemistry ,QD1-999 - Abstract
The expression and biological functions of oncofetal markers GD2 and GD3 were extensively studied in neuroectoderm-derived cancers in order to characterize their potential as therapeutic targets. Using immunological approaches, we previously identified GD3, GD2, and OAcGD2 expression in breast cancer (BC) cell lines. However, antibodies specific for O-acetylated gangliosides are not exempt of limitations, as they only provide information on the expression of a limited set of O-acetylated ganglioside species. Consequently, the aim of the present study was to use structural approaches in order to apprehend ganglioside diversity in melanoma, neuroblastoma, and breast cancer cells, focusing on O-acetylated species that are usually lost under alkaline conditions and require specific analytical procedures. We used purification and extraction methods that preserve the O-acetyl modification for the analysis of native gangliosides by MALDI-TOF. We identified the expression of GM1, GM2, GM3, GD2, GD3, GT2, and GT3 in SK-Mel28 (melanoma), LAN-1 (neuroblastoma), Hs 578T, SUM 159PT, MDA-MB-231, MCF-7 (BC), and BC cell lines over-expressing GD3 synthase. Among O-acetylated gangliosides, we characterized the expression of OAcGM1, OAcGD3, OAcGD2, OAcGT2, and OAcGT3. Furthermore, the experimental procedure allowed us to clearly identify the position of the sialic acid residue that carries the O-acetyl group on b- and c-series gangliosides by MS/MS fragmentation. These results show that ganglioside O-acetylation occurs on both inner and terminal sialic acid residue in a cell type-dependent manner, suggesting different O-acetylation pathways for gangliosides. They also highlight the limitation of immuno-detection for the complete identification of O-acetylated ganglioside profiles in cancer cells.
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- 2020
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22. Stationary time correlations for fermions after a quench in the presence of an impurity
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G. Gouraud, P. Le Doussal, and G. Schehr
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Statistical Mechanics (cond-mat.stat-mech) ,Quantum Gases (cond-mat.quant-gas) ,General Physics and Astronomy ,FOS: Physical sciences ,Condensed Matter - Quantum Gases ,Condensed Matter - Statistical Mechanics - Abstract
We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from ${\sf r}_0(k), {\sf t}_0(k)$ to ${\sf r}(k), {\sf t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\sf t}_0(k)=0$ such that the system is cut in two independent halves with ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$ respectively to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: (i) for $x=O(1)$ where the system reaches a non-equilibrium steady state (NESS) (ii) for $x \sim t$, i.e., the ray-regime. For a repulsive impurity these correlations are independent of ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$, while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions., Comment: Main text: 7 pages, 3 figures. Supp. Mat.: 31 pages, 4 figures
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- 2022
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23. Large fluctuations of the KPZ equation in a half-space
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Alexandre Krajenbrink, Pierre Le Doussal
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Physics ,QC1-999 - Abstract
We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant. These include the droplet and stationary initial conditions in full space, previously obtained by a different method. The novel results concern the droplet initial condition in a half space for several Neumann boundary conditions: hard wall, symmetric, and critical. In all cases, the height probability distribution takes the large deviation form $P(H,t) \sim \exp( - \Phi(H)/\sqrt{t})$ for small time. We obtain the rate function $\Phi(H)$ analytically for the above cases. It has a Gaussian form in the center with asymmetric tails, $|H|^{5/2}$ on the negative side, and $H^{3/2}$ on the positive side. The amplitude of the left tail for the half-space is found to be half the one of the full space. As in the full space case, we find that these left tails remain valid at all times. In addition, we present here (i) a new Fredholm Pfaffian formula for the solution of the hard wall boundary condition and (ii) two Fredholm determinant representations for the solutions of the hard wall and the symmetric boundary respectively.
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- 2018
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24. Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization
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Fyodorov, Yan V. and Le Doussal, Pierre
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- 2014
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25. Riders to the Sea de Ralph Vaughan Williams : un hymne à la mer, indomptable et indomptée, qui unit les nations
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Florence Le Doussal
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Riders to the Sea ,Williams Ralph Vaughan ,Social Sciences - Abstract
Riders to the Sea: An opera in one act based on the play by John Millington Synge, Ralph Vaughan Williams’s fifth opera, composed between 1925 and 1932, after The Poisoned Kiss (A Romantic Extravaganza), was first performed at London’s Royal College of Music on December 1st, 1937, with Malcolm Sargent conducting. A masterpiece of poetic intensity and a compendium of pain and quiet, resigned courage, worthy of a Greek tragedy, the Irish dramatist’s play was faithfully adapted by the composer-librettist in a work whose originality and universal message cannot fail to impress. Originating in his wide-ranging imagination―humanistic, brotherly, idealistic, universal―it speaks of a voyage of initiation to the Aran Islands, off the west coast of Ireland. The composer, inspired by folk wisdom and the world of the Spirit, open to worldly solicitations as well as to meditation, saw the play as a vehicle to highlight some aspects of his own musical heritage. In a few pages of dialogue, the score conveys a whole range of different emotions arising from the confrontation with Nature, and more particularly, from the forlorn struggle of the islanders against the sea and God, their ruler.
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- 2006
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26. One step replica symmetry breaking and extreme order statistics of logarithmic REMs
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Xiangyu Cao, Yan V. Fyodorov, Pierre Le Doussal
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Physics ,QC1-999 - Abstract
Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.
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- 2016
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27. Counting Function Fluctuations and Extreme Value Threshold in Multifractal Patterns: The Case Study of an Ideal 1/f Noise
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Fyodorov, Yan V., Le Doussal, Pierre, and Rosso, Alberto
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- 2012
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28. Gene expression profile predicts outcome after anthracycline-based adjuvant chemotherapy in early breast cancer
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Bertucci, François, Borie, Nathalie, Roche, Henri, Bachelot, Thomas, Le Doussal, Jean-Marc, Macgrogan, Gaëtan, Debono, Stéphane, Martinec, Agnès, Treilleux, Isabelle, Finetti, Pascal, Esterni, Benjamin, Extra, Jean-Marc, Geneve, Jean, Hermitte, Fabienne, Chabannon, Christian, Jacquemier, Jocelyne, Martin, Anne-Laure, Longy, Michel, Maraninchi, Dominique, Fert, Vincent, Birnbaum, Daniel, and Viens, Patrice
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- 2011
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29. Field Theory Conjecture for Loop-Erased Random Walks
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Fedorenko, Andrei A., Le Doussal, Pierre, and Wiese, Kay Jörg
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- 2008
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30. SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks
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Hagendorf, Christian and Le Doussal, Pierre
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- 2008
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31. Low-temperature properties of some disordered systems from the statistical properties of nearly degenerate two-level excitations
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Monthus, C. and Le Doussal, P.
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- 2004
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32. Diffusion in layered random flows, polymers, electrons in random potentials, and spin depolarization in random fields
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Le Doussal, Pierre
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- 1992
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33. Self-avoiding walks in quenched random environments
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Le Doussal, P. and Machta, J.
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- 1991
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34. Quantitative Scaling of Magnetic Avalanches
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Gianfranco Durin, Felipe Bohn, Rubem Luis Sommer, Kay Joerg Wiese, Marcio Assolin Correa, P. Le Doussal, Istituto Nazionale di Ricerca Metrologica (INRiM), Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte [Natal] (UFRN), Centro Brasileiro de Pesquisas Físicas (CBPF), Ministério da Ciência e Tecnologia, Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Magnetic domain ,FOS: Physical sciences ,General Physics and Astronomy ,01 natural sciences ,010305 fluids & plasmas ,law.invention ,symbols.namesake ,law ,0103 physical sciences ,Eddy current ,[PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn] ,Elasticity (economics) ,[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] ,010306 general physics ,Barkhausen effect ,Scaling ,Magnetic domains ,Physics ,[PHYS]Physics [physics] ,Condensed Matter - Materials Science ,Materials Science (cond-mat.mtrl-sci) ,Observable ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Amorphous solid ,Computational physics ,Granular avalanches ,Mean field theory ,symbols ,Fluctuations & noise - Abstract
We provide the first quantitative comparison between Barkhausen-noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean-field. We study different classes of soft magnetic materials: polycrystals and amorphous samples, characterized by long-range and short-range elasticity, respectively; both for thick and thin samples, i.e. with and without eddy currents. The temporal avalanche shape at fixed size, and observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents., v1: 5 pages, 6 figures; Supplemental Materials, 5 pages, 6 figures. v2+v3: updated version as published in PRL. v3: 8 pages, 12 figures. v3 corrects errors induced by a bug in assembling the pdf-files
- Published
- 2016
35. Avalanches in tip-driven interfaces in random media
- Author
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Kay Joerg Wiese, Alejandro B. Kolton, Luis E. Aragon, P. Le Doussal, Eduardo Alberto Jagla, Centro Atómico Bariloche [Argentine], Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Comisión Nacional de Energía Atómica [ARGENTINA] (CNEA), Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Magnetic domain ,Physics::Instrumentation and Detectors ,Ciencias Físicas ,Crossover ,FOS: Physical sciences ,General Physics and Astronomy ,01 natural sciences ,Numerical Simulations ,010305 fluids & plasmas ,purl.org/becyt/ford/1 [https] ,0103 physical sciences ,medicine ,Statistical physics ,[PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn] ,Elasticity (economics) ,[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] ,010306 general physics ,Scaling ,Superconductivity ,Physics ,[PHYS]Physics [physics] ,Random media ,Stiffness ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,purl.org/becyt/ford/1.3 [https] ,Condensed Matter - Disordered Systems and Neural Networks ,Vortex ,Astronomía ,medicine.symptom ,CIENCIAS NATURALES Y EXACTAS ,Depinning - Abstract
We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal exponents given by the depinning roughness exponent $\zeta$ and the interface dimension $d$, and distinct from their values in the uniformly driven case. A crossover appears between uniformly driven behaviour for small avalanches, and point driven behaviour for large avalanches. The scale of the crossover is controlled by the ratio between the stiffness of the pulling spring and the elasticity of the interface; it is visible both in the global and local avalanche-size distributions, as in the average spatial avalanche shape. Our results are relevant to model experiments involving locally driven elastic manifolds at low temperatures, such as magnetic domain walls or vortex lines in superconductors., Comment: 6 pages, 6 figures
- Published
- 2016
36. Unbinding transition in semi-infinite two-dimensional localized systems
- Author
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P. Le Doussal, M. Ortuño, and A. M. Somoza
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Semi-infinite ,Distribution (number theory) ,Logarithm ,Phase (waves) ,Conductance ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Renormalization group ,Condensed Matter Physics ,Thermal conduction ,Electronic, Optical and Magnetic Materials ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Statistical physics ,Quantum - Abstract
We consider a two-dimensional strongly localized system defined in a half-space and whose transfer integral in the edge can be different than in the bulk. We predict an unbinding transition, as the edge transfer integral is varied, from a phase where conduction paths are distributed across the bulk to a bound phase where propagation is mainly along the edge. At criticality the logarithm of the conductance follows the $F_1$ Tracy-Widom distribution. We verify numerically these predictions for both the Anderson and the Nguyen, Spivak and Shklovskii models. We also check that for a half-space, i.e., when the edge transfer integral is equal to the bulk transfer integral, the distribution of the conductance is the $F_4$ Tracy-Widom distribution. These findings are strong indications that random signs directed polymer models and their quantum extensions belong to the Kardar-Parisi- Zhang universality class. We have analyzed finite-size corrections at criticality and for a half-plane.
- Published
- 2015
- Full Text
- View/download PDF
37. Finite-temperature functional RG, droplets and decaying Burgers turbulence
- Author
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P. Le Doussal
- Subjects
Physics ,symbols.namesake ,Boundary layer ,Exact solutions in general relativity ,Random field ,Turbulence ,Quantum mechanics ,symbols ,General Physics and Astronomy ,Observable ,Function (mathematics) ,Fixed point ,Beta function - Abstract
The functional RG (FRG) approach to pinning of d-dimensional manifolds is re-examined at any temperature T. The coupling function R(u) is shown to be a physical observable in any d, exactly related to a free energy cumulant in a parabolic well. In d = 0 its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the T = 0 fixed point R(u) and its thermal boundary layer (TBL) form (i.e. for u ~ T) at T > 0. Connection between FRG in d = 0 and decaying Burgers turbulence is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any d and related to droplet probabilities.
- Published
- 2006
38. Domain Wall Creep in an Ising Ultrathin Magnetic Film
- Author
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V. Mathet, Claude Chappert, P. Le Doussal, S. Lemerle, Thierry Giamarchi, and Jacques Ferré
- Subjects
Physics ,Domain wall (magnetism) ,Magnetic domain ,Creep ,Condensed matter physics ,Exponent ,General Physics and Astronomy ,Ising model ,Correlation function (quantum field theory) ,Energy (signal processing) ,Magnetic field - Abstract
We have studied the motion of a magnetic domain wall (MDW) driven by a magnetic field H in a 2D ultrathin Pt/Co/Pt film showing perpendicular anisotropy and quenched disorder. MDW velocity measurements down to the so called creep regime show that the average energy barrier scales as $(1/H{)}^{\ensuremath{\mu}}$ with $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.24\ifmmode\pm\else\textpm\fi{}0.04$ and that the correlation function along a MDW is governed by a wandering exponent $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.69\ifmmode\pm\else\textpm\fi{}0.07$, in very good agreement with theories giving $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.25$ and $\ensuremath{\zeta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/3$. This is the first direct measurement of the creep regime for a moving interface in a disordered medium.
- Published
- 1998
39. Phase diagrams of flux lattices with disorder
- Author
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P. Le Doussal and Thierry Giamarchi
- Subjects
Physics ,Superconductivity ,Phase boundary ,Work (thermodynamics) ,Condensed matter physics ,Condensed Matter (cond-mat) ,FOS: Physical sciences ,Flux ,Condensed Matter ,Vortex ,Position (vector) ,Condensed Matter::Superconductivity ,Phase (matter) ,Phase diagram - Abstract
We review the prediction, made in a previous work [Phys. Rev. B 52 (1995)], that the phase diagram of type II superconductors consists of a topologically ordered Bragg glass phase at low fields undergoing a transition at higher fields into a vortex glass or a liquid. We estimate the position of the phase boundary using a Lindemann criterion. We find that the proposed phenomenology is compatible with recent experiments on superconductors., 7 pages 2 figures, uses epsfig
- Published
- 1997
40. Numerical study of aD-dimensional periodic Lorentz gas with universal properties
- Author
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Bouchaud, Jean-Philippe and Le Doussal, Pierre
- Published
- 1985
- Full Text
- View/download PDF
41. Nuclear characteristics as indicators of prognosis in node negative breast cancer patients
- Author
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le Doussal, V., Tubiana-Hulin, M., Hacene, K., Friedman, S., and Brunet, M.
- Published
- 1989
- Full Text
- View/download PDF
42. From equilibrium spin models to probabilistic cellular automata
- Author
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Georges, Antoine and Le Doussal, Pierre
- Published
- 1989
- Full Text
- View/download PDF
43. CP violation in very high energyp $$\bar p$$ collisions
- Author
-
Barbieri, R., Georges, A., and Le Doussal, P.
- Published
- 1986
- Full Text
- View/download PDF
44. Columnar defects and vortex fluctuations in layered superconductors
- Author
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V. M. Vinokur, P. Le Doussal, and A. E. Koshelev
- Subjects
Condensed Matter::Quantum Gases ,Josephson effect ,Superconductivity ,Materials science ,Condensed matter physics ,Plane (geometry) ,Condensed Matter (cond-mat) ,FOS: Physical sciences ,Thermal fluctuations ,Condensed Matter ,Decoupling (cosmology) ,Crystallographic defect ,Vortex ,Condensed Matter::Superconductivity ,Anisotropy - Abstract
We investigate fluctuations of Josephson-coupled pancake vortices in layered superconductors in the presence of columnar defects. We study the thermodynamics of a single pancake stack pinned by columnar defects and obtain the temperature dependence of localization length, pinning energy and critical current. We study the creep regime and compute the crossover current between line-like creep and pancake-like creep motion. We find that columnar defects effectively increase interlayer Josephson coupling by suppressing thermal fluctuations of pancakes. This leads to an upward shift in the decoupling line most pronounced around the matching field., Comment: 5 pages, REVTeX, no figures
- Published
- 1996
45. Distribution of velocities in an avalanche
- Author
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P. Le Doussal, Kay Joerg Wiese, Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Physics ,Instanton ,Statistical Mechanics (cond-mat.stat-mech) ,Spacetime ,Mathematical analysis ,FOS: Physical sciences ,General Physics and Astronomy ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,010305 fluids & plasmas ,Distribution (mathematics) ,Mean field theory ,0103 physical sciences ,[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] ,010306 general physics ,Critical dimension ,Condensed Matter - Statistical Mechanics - Abstract
For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the center-of-mass velocity is equivalent to the prediction from the ABBM stochastic equation. Our method allows to compute space and time dependence from an instanton equation. We extend the calculation beyond mean field, to lowest order in epsilon=d_uc-d., 4 pages, 2 figures
- Published
- 2011
46. Avalanches in mean-field models and the Barkhausen noise in spin-glasses
- Author
-
Markus Müller, P. Le Doussal, Kay Joerg Wiese, Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Department of Clinical Pharmacology, Medizinische Universität Wien = Medical University of Vienna, Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Physics ,Spin glass ,Condensed matter physics ,General Physics and Astronomy ,FOS: Physical sciences ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,Condensed Matter::Disordered Systems and Neural Networks ,010305 fluids & plasmas ,Magnetization ,symbols.namesake ,Mean field theory ,Phase space ,Saddle point ,[PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other] ,0103 physical sciences ,Exponent ,symbols ,010306 general physics ,Barkhausen effect ,Marginal stability - Abstract
We obtain a general formula for the distribution of sizes of "static avalanches", or shocks, in generic mean-field glasses with replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK) spin-glass it yields the density rho(S) of the sizes of magnetization jumps S along the equilibrium magnetization curve at zero temperature. Continuous replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau with exponent tau=1 for SK, related to the criticality (marginal stability) of the spin-glass phase. All scales of the ultrametric phase space are implicated in jump events. Similar results are obtained for the sizes S of static jumps of pinned elastic systems, or of shocks in Burgers turbulence in large dimension. In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple interpretation relating droplets to shocks, and a scaling theory for the equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are discussed., Comment: 6 pages, 1 figure
- Published
- 2010
- Full Text
- View/download PDF
47. Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
- Author
-
Alberto Rosso, P. Le Doussal, Yan V. Fyodorov, School of Mathematical Sciences [Nottingham], University of Nottingham, UK (UON), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Phase transition ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,Phase (waves) ,General Physics and Astronomy ,Duality (optimization) ,FOS: Physical sciences ,Probability density function ,01 natural sciences ,010305 fluids & plasmas ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,0103 physical sciences ,Statistical physics ,Symmetry breaking ,[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Mathematical Physics ,Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Turbulence ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Mathematical Physics (math-ph) ,Condensed Matter - Disordered Systems and Neural Networks ,Nonlinear Sciences - Chaotic Dynamics ,Distribution (mathematics) ,[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] ,Chaotic Dynamics (nlin.CD) ,Random matrix - Abstract
We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model., Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figures
- Published
- 2010
- Full Text
- View/download PDF
48. Tethered membranes with long-range self-avoidance: large-dimension limit
- Author
-
P. Le Doussal
- Subjects
Physics ,Phase transition ,Range (particle radiation) ,Isotropy ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Statistical mechanics ,Condensed Matter::Soft Condensed Matter ,Membrane ,Classical mechanics ,Dimension (vector space) ,Embedding ,Limit (mathematics) ,Mathematical Physics - Abstract
The influence of long-range self-avoiding forces on the statistical mechanics of a D-dimensional tethered membrane is studied in the limit of large embedding space dimension d to infinity . The author finds three distinct isotropic (crumpled) phases and several flat phases, and thermally driven crumpling transitions for D>2. The effect of attraction and of short-range repulsion for D>2 is also discussed.
- Published
- 1992
49. Self-avoiding walks in quenched random environments
- Author
-
P. Le Doussal and Jonathan Machta
- Subjects
Renormalization ,Condensed matter physics ,Percolation ,Path (graph theory) ,Statistical and Nonlinear Physics ,Statistical mechanics ,State (functional analysis) ,Renormalization group ,Fixed point ,Mathematical Physics ,Self-avoiding walk ,Mathematics - Abstract
The self-avoiding walk in a quenched random environment is studied using realspace and field-theoretic renormalization and "Flory" arguments. These methods indicate that the system is described, for d de, by a strong disorder fixed point corresponding to a "glass" state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk, L ~ N ~ with N the number of steps, and the fluctuations in the free energy, Af~ L% The bound 1/~ - co ~pore and suggests that this inequality holds for d = 2 and 3, although ~ = ~pure cannot be excluded, particularly for d= 2. For d> d c there is a transition between strong and weak disorder phases at which ~ = ~pure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized.
- Published
- 1991
50. Statistical Mechanics of Directed Polymer Melts
- Author
-
David R. Nelson and P. Le Doussal
- Subjects
Condensed Matter::Soft Condensed Matter ,Physics ,chemistry.chemical_classification ,Classical mechanics ,chemistry ,Quantum mechanics ,Structure function ,General Physics and Astronomy ,Statistical mechanics ,Polymer ,External source ,Boson - Abstract
Solutions of variable-length directed polymers are studied via a mapping onto the quantum mechanics of bosons with an external source in two dimensions. The theory is applicable, in particular, to entangled polymer nematics. We calculate the structure function of these systems, and the renormalized Frank constants.
- Published
- 1991
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