Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

Pseudorandomness When the Odds are Against You

Impagliazzo and Wigderson (STOC 1997) showed that if E=DTIME(2^O(n)) requires size 2^Omega(n) circuits, then every time T constant-error randomized algorithm can be simulated deterministically in time poly(T). However, such polynomial slowdown is a deal breaker when T=2^(alpha*n), for a constant alpha>0, as is the case for some randomized algorithms for NP-complete problems. Paturi and Pudlak (STOC 2010) observed that many such algorithms are obtained from randomized time T algorithms, for T < 2^o(n), with large one-sided error 1-epsilon, for epsilon=2^(-alpha*n), that are repeated 1/epsilon times to yield a constant-error randomized algorithm running in time T/epsilon=2^((alpha+o(1))*n). We show that if E requires size 2^Omega(n) nondeterministic circuits, then there is a poly(n)-time epsilon-HSG (Hitting-Set Generator) H:{0,1}^(O(log(n)) + log(1/epsilon) -> {0,1}^n, implying that time T randomized algorithms with one-sided error 1-epsilon can be simulated in deterministic time poly(T)/epsilon. In particular, under this hardness assumption, the fastest known constant-error randomized algorithm for k-SAT (for k > 3) by Paturi et al. (J. ACM 2005) can be made deterministic with essentially the same time bound. This is the first hardness versus randomness tradeoff for algorithms for NP-complete problems. We address the necessity of our assumption by showing that HSGs with very low error imply hardness for nondeterministic circuits with "few" nondeterministic bits. Applebaum et al. (CCC 2015) showed that "black-box techniques" cannot achieve poly(n)-time computable epsilon-PRGs (Pseudo-Random Generators) for epsilon=n^-omega(1), even if we assume hardness against circuits with oracle access to an arbitrary language in the polynomial time hierarchy. We introduce weaker variants of PRGs with relative error, that do follow under the latter hardness assumption. Specifically, we say that a function G:{0,1}^r -> {0,1}^n is an (epsilon,delta)-re-PRG for a circuit C if (1-epsilon)*Pr[C(U_n)=1] - delta < Pr[C(G(U_r)=1] < (1+epsilon)*Pr[C(U_n)=1] + delta. We construct poly(n)-time computable (epsilon,delta)-re-PRGs with arbitrary polynomial stretch, epsilon=n^-O(1) and delta=2^(-n^Omega(1)). We also construct PRGs with relative error that fool non-boolean distinguishers (in the sense introduced by Dubrov and Ishai (STOC 2006)). Our techniques use ideas from Paturi and Pudlak (STOC 2010), Trevisan and Vadhan (FOCS 2000), Applebaum et al. (CCC 2015). Common themes in our proofs are "composing" a PRG/HSG with a combinatorial object such as dispersers and extractors, and the use of nondeterministic reductions in the spirit of Feige and Lund (Comp. Complexity 1997)

Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterministic Reductions (Extended Abstract)

A circuit C compresses a function f:{0,1}^n -> {0,1}^m if given an input x in {0,1}^n the circuit C can shrink x to a shorter l-bit string x\u27 such that later, a computationally-unbounded solver D will be able to compute f(x) based on x\u27. In this paper we study the existence of functions which are incompressible by circuits of some fixed polynomial size s=n^c. Motivated by cryptographic applications, we focus on average-case (l,epsilon) incompressibility, which guarantees that on a random input x in {0,1}^n, for every size s circuit C:{0,1}^n -> {0,1}^l and any unbounded solver D, the success probability Pr_x[D(C(x))=f(x)] is upper-bounded by 2^(-m)+epsilon. While this notion of incompressibility appeared in several works (e.g., Dubrov and Ishai, STOC 06), so far no explicit constructions of efficiently computable incompressible functions were known. In this work we present the following results: 1. Assuming that E is hard for exponential size nondeterministic circuits, we construct a polynomial time computable boolean function f:{0,1}^n -> {0,1} which is incompressible by size n^c circuits with communication l=(1-o(1)) * n and error epsilon=n^(-c). Our technique generalizes to the case of PRGs against nonboolean circuits, improving and simplifying the previous construction of Shaltiel and Artemenko (STOC 14). 2. We show that it is possible to achieve negligible error parameter epsilon=n^(-omega(1)) for nonboolean functions. Specifically, assuming that E is hard for exponential size Sigma_3-circuits, we construct a nonboolean function f:{0,1}^n -> {0,1}^m which is incompressible by size n^c circuits with l=Omega(n) and extremely small epsilon=n^(-c) * 2^(-m). Our construction combines the techniques of Trevisan and Vadhan (FOCS 00) with a new notion of relative error deterministic extractor which may be of independent interest. 3. We show that the task of constructing an incompressible boolean function f:{0,1}^n -> {0,1} with negligible error parameter epsilon cannot be achieved by "existing proof techniques". Namely, nondeterministic reductions (or even Sigma_i reductions) cannot get epsilon=n^(-omega(1)) for boolean incompressible functions. Our results also apply to constructions of standard Nisan-Wigderson type PRGs and (standard) boolean functions that are hard on average, explaining, in retrospective, the limitations of existing constructions. Our impossibility result builds on an approach of Shaltiel and Viola (SIAM J. Comp., 2010)

Compression of microwave pulses in a resonant system based on two waveguide T-joints

Research results for a resonant microwave compressor consisting of two waveguide T-joints are presented. When feeding the compressor with the help of a pulse magnetron with 2 MW power and 3.2 μs duration of microwave pulses the maximum power gain of 23 dB and the peak power of 400 MW is obtained in S-band for the 4 μs long pulses

Definition of optimal parameters of resonance SHF-compressors

There is represented the simplest methodology of calculation of super high frequency (SHF) compressors optimal parameters. In generalized form there are represented analytical expressions for definition of main energy characteristics of SHF-compressors. Calculation results are shown in graphic form, which allows to define practically all optimal parameters of SHF-compression devices, using initial data

Analysis of microwave energy extraction process at the resonator with controlled transformation of oscillation modes

It is considered an operation of resonance microwave compressor with extraction of energy by means of controlled transformation of oscillations modes on a coupling window of the resonator with short-cut waveguide stub. Using dispersion matrix method with a device model we carried out the analysis of the extraction process in case of transformation of high-Q mode into down to the limit low-Q mode. There are obtained the expressions for description of the transient processes during accumulation and extraction processes. It is shown researched compressor is possible to shape the microwave pulses with controlled power, duration and envelope shape

Influence of Dy and Ho on the Phase Composition of the Ti-Al System Obtained by ‘Hydride Technology’

The manuscript describes the phase composition, microstructure, some physical and mechanical properties of the Ti-Al system with addition of 2 at. % Dy (TAD) and Ho (TAH) obtained by “hydride technology”. Phase diagrams for Ti-Al-Dy and Ti-Al-Ho at a temperature of 1150 °C and basic properties for ternary phases Dy₆Ti₄Al₄₃ and Ho₆Ti₄Al₄₃ were calculated. A crystallographic database of stable and quasistable structures of the known elemental composition was created in the USPEX-SIESTA software by means of an evolutionary code. The calculations show that adding REM leads to a significant stabilizing effect in each Ti-Al-Me (Me = Dy, Ho) system without exception. It has been established that the lattice energies of AlTi3Ho and AlTi3Dy are, respectively, equal to: EAl4Ti12Dy3 = −32,877.825 eV and EAl4Ti12Dy3 = −31,227.561 eV. In the synthesized Ti49Al49Ho2 compound, the main phases include Al-Ti, Al3Ti3 and Al4Ti12Ho3 and the contributions to the theoretical intensity are equal to 44.83, 44.43 and 5.55%, respectively. Ti49Al49Dy2 is dominated by the Al-Ti, Al3Ti3 and Al4Ti12Dy phases, whose contributions are equal to 65.04, 16.88 and 11.2%, respectively. The microhardness of TAD and TAN specimens is 1.61 ± 0.08 and 1.47 ± 0.07 GPa, respectively