Spectral Statistics in the Quantized Cardioid Billiard

The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good agreement with the GOE distribution of random-matrix theory. In case of the number variance and rigidity we observe agreement with the random-matrix model for short-range correlations only, whereas for long-range correlations both statistics saturate in agreement with semiclassical expectations. Furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal Gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes. By means of the Gutzwiller trace formula the trace of the cosine-modulated heat kernel is studied. Since the billiard boundary is focusing there are conjugate points giving rise to zeros at the locations of the periodic orbits instead of exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil

Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons

Nonclassical phase-space trajectories for the damped harmonic quantum oscillator

The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.Comment: 8 pages, 3 figures, accepted for publication in Chemical Physic

Decay of Classical Chaotic Systems - the Case of the Bunimovich Stadium

The escape of an ensemble of particles from the Bunimovich stadium via a small hole has been studied numerically. The decay probability starts out exponentially but has an algebraic tail. The weight of the algebraic decay tends to zero for vanishing hole size. This behaviour is explained by the slow transport of the particles close to the marginally stable bouncing ball orbits. It is contrasted with the decay function of the corresponding quantum system.Comment: 16 pages, RevTex, 3 figures are available upon request from [email protected], to be published in Phys.Rev.

Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.Comment: 4 pages, 6 figure

Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

Reply

Reply. We are grateful for the interest others have shown in our paper, which allowed us to clarify critical aspects of the case-control study design and the nature of our study population

No Association Between Screening for Hepatocellular Carcinoma and Reduced Cancer-Related Mortality in Patients With Cirrhosis

Background & Aims: Screening patients with cirrhosis for hepatocellular carcinoma (HCC) has been recommended. We conducted a matched case–control study within the US Veterans Affairs (VA) health care system to determine whether screening by abdominal ultrasonography (USS) and/or by measuring serum level of α-fetoprotein (AFP) was associated with decreased cancer-related mortality in patients with cirrhosis. Methods: We defined cases (n = 238) as patients with cirrhosis who died of HCC from January 1, 2013 through August 31, 2015 and had been in VA care with a diagnosis of cirrhosis for at least 4 years before the diagnosis of HCC. We matched each case to 1 control (n = 238), defined as a patient with cirrhosis who did not die of HCC and had been in VA care for at least 4 years before the date of the matched case's HCC diagnosis. Controls were matched to cases by year of cirrhosis diagnosis, race and ethnicity, age, sex, etiology of cirrhosis, Model for End-Stage Liver Disease score, and VA medical center. We identified all USS and serum AFP tests performed within 4 years before the date of HCC diagnosis in cases or the equivalent index date in controls and determined by chart extraction (blinded to case or control status) whether these tests were performed for screening. Results: There were no significant differences between cases and controls in the proportions of patients who underwent screening USS (52.9% vs 54.2%), screening measurement of serum AFP (74.8% vs 73.5%), screening USS or measurement of serum AFP (81.1% vs 79.4%), or screening USS and measurement of serum AFP (46.6% vs 48.3%) within 4 years before the index date, with or without adjusting for potential confounders. There also was no difference in receipt of these screening tests within 1, 2, or 3 years before the index date. Conclusions: In a matched case–control study of the VA health care system, we found that screening patients with cirrhosis for HCC by USS, measurement of serum AFP, either test, or both tests was not associated with decreased HCC-related mortality. We encourage additional case–control studies to evaluate the efficacy of screening for HCC in other health care systems, in which available records are sufficiently detailed to enable identification of the indication for USS and AFP tests

Survival, pathologic response, and genomics in CALGB 40601 (Alliance), a neoadjuvant Phase III trial of paclitaxel-trastuzumab with or without lapatinib in HER2-positive breast cancer

PURPOSE CALGB 40601 assessed whether dual versus single human epidermal growth factor receptor 2 (HER2) -targeting drugs added to neoadjuvant chemotherapy increased pathologic complete response (pCR). Here, we report relapse-free survival (RFS), overall survival (OS), and gene expression signatures that predict pCR and survival. PATIENTS AND METHODS Three hundred five women with untreated stage II and III HER2-positive breast cancer were randomly assigned to receive weekly paclitaxel combined with trastuzumab plus lapatinib (THL), trastuzumab (TH), or lapatinib (TL). The primary end point was pCR, and secondary end points included RFS, OS, and gene expression analyses. mRNA sequencing was performed on 264 pretreatment samples. RESULTS One hundred eighteen patients were randomly allocated to THL, 120 to TH, and 67 to TL. At more than 7 years of follow-up, THL had significantly better RFS and OS than did TH (RFS hazard ratio, 0.32; 95% CI, 0.14 to 0.71; P 5.005; OS hazard ratio, 0.34; 95% CI, 0.12 to 0.94; P 5.037), with no difference between TH and TL. Of 688 previously described gene expression signatures, significant associations were found in 215 with pCR, 45 with RFS, and only 22 with both pCR and RFS (3.2%). Specifically, eight immune signatures were significantly correlated with a higher pCR rate and better RFS. Among patients with residual disease, the immunoglobulin G signature was an independent, good prognostic factor, whereas the HER2-enriched signature, which was associated with a higher pCR rate, showed a significantly shorter RFS. CONCLUSION In CALGB 40601, dual HER2-targeting resulted in significant RFS and OS benefits. Integration of intrinsic subtype and immune signatures allowed for the prediction of pCR and RFS, both overall and within the residual disease group. These approaches may provide means for rational escalation and de-escalation treatment strategies in HER2-positive breast cancer