&lt;title&gt;Recent advances in holographic materials from Slavich&lt;/title&gt;

Zacharovas, Stanislovas; Ratcliffe, David B.; Skokov, Gleb R.; Vorobyov, Sergey P.; Kumonko, Petr I.; Sazonov, Yury A.

doi:10.1117/12.342818

Cited by 7 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in terms of the components of the high-frequency conductivity tensor σ(k, ω). Equation (1) has been established by a number of authors and by different methods (Sazonov & Tsytovitch 1968;Heyvaerts 1969;Zheleznyakov, Suzorov & Shaposhnikov 1974). A direct derivation of the absorption-like term is presented below.…”

Section: Description Of Polarization Transfermentioning

confidence: 99%

See 1 more Smart Citation

Polarization transfer in relativistic magnetized plasmas

Heyvaerts¹,

Prunet²,

Thiébaut³

2013

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

The polarization transfer coefficients of a relativistic magnetized plasma are derived. These results apply to any momentum distribution function of the particles, isotropic or anisotropic. Particles interact with the radiation either in a non-resonant mode when the frequency of the radiation exceeds their characteristic synchrotron emission frequency, or quasi-resonantly otherwise. These two classes of particles contribute differently to the polarization transfer coefficients. For a given frequency, this dichotomy corresponds to a regime change in the dependence of the transfer coefficients on the parameters of the particle's population, since these parameters control the relative weight of the contribution of each class of particles. Our results apply to either regimes as well as the intermediate one. The derivation of the transfer coefficients involves an exact expression of the conductivity tensor of the relativistic magnetized plasma that has not been used hitherto in this context. Suitable expansions valid at frequencies much larger than the cyclotron frequency allow us to analytically perform the summation over all resonances at high harmonics of the relativistic gyrofrequency.The transfer coefficients are represented in the form of two-variable integrals that can be conveniently computed for any set of parameters by using Olver's expansion of high-order Bessel functions. We particularize our results to a number of distribution functions, isotropic, thermal or power-law, with different multipolar anisotropies of low order, or strongly beamed. Specifically, earlier exact results for thermal distributions are recovered. For isotropic distributions, the Faraday coefficients are expressed in the form of a one-variable quadrature over energy, for which we provide the kernels in the high-frequency limit and in the asymptotic low-frequency limit. An interpolation formula extending over the full energy range is proposed for these kernels. A similar reduction to a one-variable quadrature over energy is derived at high frequency for a large class of anisotropic distribution functions that may form a basis on which any smoothly anisotropic distribution could be expanded.

show abstract

Section: Description Of Polarization Transfermentioning

confidence: 99%

“…A direct derivation of the absorption-like term is presented below. The derivation of the emission term is less straightforward (Sazonov & Tsytovitch 1968).…”

Section: Description Of Polarization Transfermentioning

confidence: 99%

Polarization transfer in relativistic magnetized plasmas

Heyvaerts¹,

Prunet²,

Thiébaut³

2013

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

show abstract

“…The investigation of limit theorems for Lyapunov exponents has a long history, see e.g. [57], [15] and the references therein. Interest in this area has resurged more recently due to explicit results for finite products [4,24,26,36,40,55].…”

Section: Introductionmentioning

confidence: 99%

Products of random matrices from polynomial ensembles

Kieburg¹,

Kösters²

2019

Ann. Inst. H. Poincaré Probab. Statist.

View full text Add to dashboard Cite

Very recently we have shown that the spherical transform is a convenient tool for studying the relation between the joint density of the singular values and that of the eigenvalues for bi-unitarily invariant random matrices. In the present work we discuss the implications of these results for products of random matrices. In particular, we derive a transformation formula for the joint densities of a product of two independent bi-unitarily invariant random matrices, the first from a polynomial ensemble and the second from a polynomial ensemble of derivative type. This allows us to re-derive and generalize a number of recent results in random matrix theory, including a transformation formula for the kernels of the corresponding determinantal point processes. Starting from these results, we construct a continuous family of random matrix ensembles interpolating between the products of different numbers of Ginibre matrices and inverse Ginibre matrices. Furthermore, we make contact to the asymptotic distribution of the Lyapunov exponents of the products of a large number of bi-unitarily invariant random matrices of fixed dimension.

show abstract

“…In several works, e.g. [10,[40][41][42][43], it has been shown for various kinds of X j being i.i.d. that the distributions of the Lyapunov exponents λ j become asymptotically Gaussian when choosing M N .…”

mentioning

confidence: 99%

From integrable to chaotic systems: Universal local statistics of Lyapunov exponents

Akemann¹,

Burda²,

Kieburg³

2019

EPL

View full text Add to dashboard Cite

Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independent random N ×N matrix with complex Gaussian elements, the complex Ginibre ensemble. This model allows to explicitly compute the Lyapunov exponents and local correlations amongst them, when the number of factors M becomes large. While the smallest eigenvalues always remain deterministic, which is also the case for many chaotic quantum systems, we identify a critical double scaling limit N ∼ M for the rest of the spectrum. It interpolates between the known deterministic behaviour of the Lyapunov exponents for M N (or N fixed) and universal random matrix statistics for M N (or M fixed), characterising chaotic behaviour. After unfolding this agrees with Dyson's Brownian Motion starting from equidistant positions in the bulk and at the soft edge of the spectrum. This universality statement is further corroborated by numerical experiments, multiplying different kinds of random matrices. It leads us to conjecture a much wider applicability in complex systems, that display a transition from deterministic to chaotic behaviour.

show abstract

<title>Recent advances in holographic materials from Slavich</title>

Cited by 7 publications

References 0 publications

Polarization transfer in relativistic magnetized plasmas

Polarization transfer in relativistic magnetized plasmas

Products of random matrices from polynomial ensembles

From integrable to chaotic systems: Universal local statistics of Lyapunov exponents

Contact Info

Product

Resources

About