Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach

We deduce the effects of quantum interference on the conductance of chaotic cavities by using a statistical ansatz for the S matrix. Assuming that the circular ensembles describe the S matrix of a chaotic cavity, we find that the conductance fluctuation and weak-localization magnitudes are universal: they are independent of the size and shape of the cavity if the number of incoming modes, N, is large. The limit of small N is more relevant experimentally; here we calculate the full distribution of the conductance and find striking differences as N changes or a magnetic field is applied.Comment: 4 pages revtex 3.0 (2-column) plus 2 postscript figures (appended), hub.pam.94.

Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption

We quantify the presence of direct processes in the S-matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{i\theta}, is studied in cavities with time-reversal symmetry for different antenna coupling strengths T_a or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations based on the Heidelberg approach including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with random-matrix predictions for all cases.Comment: 4 pages, 4 figure

Wave Scattering through Classically Chaotic Cavities in the Presence of Absorption: An Information-Theoretic Model

We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint $=\alpha n$: n is the dimensionality of S, and $0\leq \alpha \leq 1, \alpha =0(1)$ meaning complete (no) absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential -Rayleigh statistics- even for n=1. For $n\gg 1$ Rayleigh statistics is attained even with no absorption; here we extend the study to $\alpha <1$. The model is compared with random-matrix-theory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. Thus, in the latter regime, some important physical constraint is missing in the construction of the model.Comment: 4 pages, latex, 3 ps figure

Path Integral Approach to the Scattering Theory of Quantum Transport

The scattering theory of quantum transport relates transport properties of disordered mesoscopic conductors to their transfer matrix \bbox{T}. We introduce a novel approach to the statistics of transport quantities which expresses the probability distribution of \bbox{T} as a path integral. The path integal is derived for a model of conductors with broken time reversal invariance in arbitrary dimensions. It is applied to the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation which describes quasi-one-dimensional wires. We use the equivalent channel model whose probability distribution for the eigenvalues of \bbox{TT}^{\dagger} is equivalent to the DMPK equation independent of the values of the forward scattering mean free paths. We find that infinitely strong forward scattering corresponds to diffusion on the coset space of the transfer matrix group. It is shown that the saddle point of the path integral corresponds to ballistic conductors with large conductances. We solve the saddle point equation and recover random matrix theory from the saddle point approximation to the path integral.Comment: REVTEX, 9 pages, no figure

Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry

The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been believed that Anderson localization inevitably arises in ordinary disordered wires. A counterexample is recently found in the systems with symplectic symmetry, where one perfectly conducting channel is present even in the long-wire limit when the number of conducting channels is odd. This indicates that the odd-channel case is essentially different from the ordinary even-channel case. To study such differences, we derive the DMPK equation for transmission eigenvalues for both the even- and odd- channel cases. The behavior of dimensionless conductance is investigated on the basis of the resulting equation. In the short-wire regime, we find that the weak-antilocalization correction to the conductance in the odd-channel case is equivalent to that in the even-channel case. We also find that the variance does not depend on whether the number of channels is even or odd. In the long-wire regime, it is shown that the dimensionless conductance in the even-channel case decays exponentially as --> 0 with increasing system length, while --> 1 in the odd-channel case. We evaluate the decay length for the even- and odd-channel cases and find a clear even-odd difference. These results indicate that the perfectly conducting channel induces clear even-odd differences in the long-wire regime.Comment: 28pages, 5figures, Accepted for publication in J. Phys. Soc. Jp

Conductance of Disordered Wires with Symplectic Symmetry: Comparison between Odd- and Even-Channel Cases

The conductance of disordered wires with symplectic symmetry is studied by numerical simulations on the basis of a tight-binding model on a square lattice consisting of M lattice sites in the transverse direction. If the potential range of scatterers is much larger than the lattice constant, the number N of conducting channels becomes odd (even) when M is odd (even). The average dimensionless conductance g is calculated as a function of system length L. It is shown that when N is odd, the conductance behaves as g --> 1 with increasing L. This indicates the absence of Anderson localization. In the even-channel case, the ordinary localization behavior arises and g decays exponentially with increasing L. It is also shown that the decay of g is much faster in the odd-channel case than in the even-channel case. These numerical results are in qualitative agreement with existing analytic theories.Comment: 4 page

Measurements and analysis of the upper critical field Hc2H_{c2} on an underdoped and overdoped La2−xSrxCuO4La_{2-x}Sr_xCuO_4 compounds

The upper critical field $H_{c2}$ is one of the many non conventional properties of high-$T_c$ cuprates. It is possible that the $H_{c2}(T)$ anomalies are due to the presence of inhomogeneities in the local charge carrier density $\rho$ of the $CuO_2$ planes. In order to study this point, we have prepared good quality samples of polycrystalline $La_{2-x}Sr_xCuO_{4}$ using the wet-chemical method, which has demonstrated to produce samples with a better cation distribution. In particular, we have studied the temperature dependence of the second critical field, $H_{c2}(T)$, through the magnetization measurements on two samples with opposite average carrier concentration ($\rho_m=x$) and nearly the same critical temperature, namely $\rho_m = 0.08$ (underdoped) and $\rho_m = 0.25$ (overdoped). The results close to $T_c$ do not follow the usual Ginzburg-Landau theory and are interpreted by a theory which takes into account the influence of the inhomogeneities.Comment: Published versio

Diagonal approximation of the form factor of the unitary group

The form factor of the unitary group U(N) endowed with the Haar measure characterizes the correlations within the spectrum of a typical unitary matrix. It can be decomposed into a sum over pairs of ``periodic orbits'', where by periodic orbit we understand any sequence of matrix indices. From here the diagonal approximation can be defined in the usual fashion as a sum only over pairs of identical orbits. We prove that as we take the dimension $N$ to infinity, the diagonal approximation becomes ``exact'', that is converges to the full form factor.Comment: 9 page

Ballistic Transport Through Chaotic Cavities: Can Parametric Correlations and the Weak Localization Peak be Described by a Brownian Motion Model?

A Brownian motion model is devised on the manifold of S-matrices, and applied to the calculation of conductance-conductance correlations and of the weak localization peak. The model predicts that (i) the correlation function in $B$ has the same shape and width as the weak localization peak; (ii) the functions behave as $\propto 1-{\cal O}(B^2)$, thus excluding a linear line shape; and (iii) their width increases as the square root of the number of channels in the leads. Some of these predictions agree with experiment and with other calculations only in the limit of small $B$ and a large number of channels.Comment: 5 pages revtex (twocolumn