Random matrix theory and critical phenomena in quantum spin chains

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators 〈σ_{i}^{x}σ_{i+n}^{x}〉_{g},〈σ_{i}^{y}σ_{i+n}^{y}〉_{g}, and 〈∏_{i=1}^{n}σ_{i}^{z}〉_{g}, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

Number fields and function fields: coalescences, contrasts and emerging applications

The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field. Although an active area of interaction for the past half century at least, the language and techniques used in analytic number theory and in the function field setting are quite different, and this has frustrated interchanges between the two areas. This situation is currently changing, and there has been substantial progress on a number of problems stimulated by bringing together ideas from each field. We here introduce the papers published in this Theo Murphy meeting issue, where some of the recent developments are explained.

Quantum chaotic resonances from short periodic orbits

We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest-living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long-lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.

Quantum ergodicity on graphs

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear sigma model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.

CT manifestations of ileal dysgenesis

Ileal dysgenesis is an uncommon condition of unknown etiology occurring in the distal ileum in the region of the vitelline duct. The CT appearance of this lesion, although not previously described to our knowledge, is characteristic. We report a patient with ileal dysgenesis who had an abdominal CT scan to evaluate chronic iron deficiency anemia and protein-losing enteropathy. Recognition of this lesion by pediatric radiologists is important; so that surgical treatment, which is simple and effective, can be initiated quickly.

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Planck's over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Planck's over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker's map, for which the probability density in position space is observed to have self-similarity properties.

Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by stochastic Loewner evolution with diffusion constant close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.

Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa as N-->infinity, where kappa and kappa are determined explicitly. In an important class of systems, kappa is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for kappa therefore provides an explicit formula for the central charge.

Intermediate wave function statistics

We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred, in the case of star graphs by short (unstable) periodic orbits and, in the case of Seba billiards, by certain families of orbits. We construct sequences of states which have such a limit. Our results are illustrated by numerical computations.

Persistent hyperlipasemia caused by macrolipase in an adolescent

Serum amylase and lipase frequently rise during bouts of acute pancreatitis, and measurement of these enzymes provides important diagnostic information. We report a pediatric patient with persistent elevations of serum lipase resulting from macrolipasemia, a complex of lipase with IgG, rather than pancreatitis.

A multicentre retrospective audit of outcome of patients undergoing curative resection for rectal cancer

AIM

This study describes the outcome of patients with rectal cancer treated in four New Zealand public hospitals before the advent of specialised colorectal units in order to provide a baseline against which any changes in management can be measured.

METHODS

A retrospective review of case notes of patients who underwent resection of rectal cancer with curative intent over a period of 7-10 years up to 1995 in Christchurch, Wellington, Nelson, and Masterton Public Hospital's, was undertaken. Patients were identified from hospital records using a combination of methods (pathology data bases, clinical case mix data, operating logs and audit data). Metastatic disease was considered to be present if confirmed on histology or the clinical course of the patient was consistent with metastatic disease. Patients were excluded if there was perioperative evidence of metastatic disease or if they had transanal excision. Previously published results from Auckland and Dunedin Hospitals are compared.

RESULTS

524 patients with rectal cancer were identified who had undergone surgery with curative intent in the four hospitals. The overall permanent stoma rate was 37%. The overall 30-day mortality was 2.9%, five-year survival was 63% and local recurrence at five years was 26%.

CONCLUSION

While low perioperative mortality and good long-term survival were achieved, there were high rates of local recurrence. These data are a baseline against which the impact of new approaches to curative resection for rectal cancer can be measured.

Use of ultrasonic surgical aspirator in operative cytoreduction of pseudomyxoma peritonei

Pseudomyxoma peritonei presents a unique challenge to the surgical oncologist. Residual gelatinous tumor with varying degrees of adherence always remains on the abdominal viscera after standard excisional therapy. Traditionally, this has been removed by "electroevaporation" with ball-tip diathermy, but this is associated with an extensive peritoneal burn and associated ileus. We describe the use of an ultrasonic surgical aspirator as a safe and efficient method of tumor removal in this condition.

Complete genomic structure and mutational spectrum of PHKA2 in patients with x-linked liver glycogenosis type I and II

X-linked liver glycogenosis (XLG) is probably the most frequent glycogen-storage disease. XLG can be divided into two subtypes: XLG I, with a deficiency in phosphorylase kinase (PHK) activity in peripheral blood cells and liver; and XLG II, with normal in vitro PHK activity in peripheral blood cells and with variable activity in liver. Both types of XLG are caused by mutations in the same gene, PHKA2, that encodes the regulatory alpha subunit of PHK. To facilitate mutation analysis in PHKA2, we determined its genomic structure. The gene consists of 33 exons, spanning >/=65 kb. By SSCP analysis of the different PHKA2 exons, we identified five new XLG I mutations, one new XLG II mutation, and one mutation present in both a patient with XLG I and a patient with XLG II, bringing the total to 19 XLG I and 12 XLG II mutations. Most XLG I mutations probably lead to truncation or disruption of the PHKA2 protein. In contrast, all XLG II mutations are missense mutations or small in-frame deletions and insertions. These results suggest that the biochemical differences between XLG I and XLG II might be due to the different nature of the disease-causing mutations in PHKA2. XLG I mutations may lead to absence of the alpha subunit, which causes an unstable PHK holoenzyme and deficient enzyme activity, whereas XLG II mutations may lead to in vivo deregulation of PHK, which might be difficult to demonstrate in vitro.

Vasculitis-induced colonic strictures: report of two cases

PURPOSE

The clinical presentations of gastrointestinal involvement from systemic vasculitis are diverse. Colonic involvement from systemic vasculitis is unusual. We report the first case of a symptomatic colonic stricture associated with rheumatoid vasculitis and another associated with systemic lupus erythematosus.

METHODS

The clinical, radiologic, and histologic features of two cases of symptomatic colonic strictures secondary to colonic involvement with vasculitis are described. The literature covering gastrointestinal involvement from vasculitis in these conditions is reviewed.

RESULTS

Surgical resection of the colonic strictures was required in both patients and had a satisfactory outcome.

CONCLUSIONS

These cases provide further evidence of the protean clinical presentations of intestinal involvement in systemic vasculitis. Although immunosuppression has been shown to be of value in the treatment of vasculitis affecting the gastrointestinal tract, surgical resection is required for established strictures.

Sclerosing encapsulating peritonitis after intraperitoneal use of povidone iodine

BACKGROUND

The use of intraperitoneal povidone iodine as an agent for peritoneal lavage in colorectal surgery is controversial. Although it possesses a wide range of antimicrobial activity and is rapidly lethal to dissociated colorectal cancer cells in vitro, concern about its potential toxicity remains.

METHODS

Two cases of sclerosing encapsulating peritonitis (SEP) following elective colorectal surgery are presented. In each case the peritoneal cavity was lavaged with an aqueous povidone iodine solution. The surgical literature on the intraperitoneal use of povidone iodine is reviewed.

RESULTS

Significant morbidity resulted from the postoperative development of SEP in both of our patients. In one patient an ileo-anal pouch could not be fashioned following an initial colectomy, and in the second patient a small-bowel obstruction required a laparotomy and a period of intravenous nutrition before an oral diet could be tolerated.

CONCLUSION

The use of povidone iodine for peritoneal lavage in colorectal surgery is to be cautioned against in concentrations of > 1%.

Hydrodissection: an easy way to dissect anatomical planes and complex adhesions

BACKGROUND

Sharp dissection of adherent tissues resulting from previous sepsis or surgery is frequently time-consuming and sometimes difficult.

METHODS

The introduction of saline under pressure into the plane of dissection facilitates this task.

RESULTS

Hydrodissection both creates and displays the correct plane between adherent tissues.

CONCLUSIONS

This technique increases the safety and decreases the time spent in adhesiolysis in re-operative surgery.

Are special investigations of value in the management of patients with fecal incontinence?

PURPOSE

The aim of this study was to determine whether special investigations significantly alter either the diagnosis or the management plan of patients with fecal incontinence assessed on the basis of a structured history and physical examination alone.

METHODS

Fifty consecutive patients with fecal incontinence were prospectively studied in a tertiary referral clinic. Each patient was assessed by two clinicians who independently formulated a diagnosis and treatment plan based on the history and physical examination. The resulting 100 patient assessments were then compared with the final diagnosis and treatment plan formulated on completion of endoanal ultrasound, anal manometry, external sphincter electromyography, and defecating proctography.

RESULTS

In the assessment of fecal incontinence, the addition of special investigations altered the diagnosis of the cause of incontinence based on history and examination alone in 19 percent of cases. The management plan was altered in 16 percent of cases. Special investigations were most useful in separating neuropathy from rectal wall disorders and in demonstrating the unexpected presence of internal sphincter defects and neuropathy.

CONCLUSIONS

Even experienced colorectal surgeons will misdiagnose up to one-fifth of patients presenting with fecal incontinence if assessment is based on the history and physical examination alone. However surgically correctable causes of incontinence are rarely missed on clinical assessment.

Laparoscopic resection of the colon and rectum for cancer

BACKGROUND

Laparoscopically-assisted resection for large bowel cancer is technically feasible. Sixty-six patients who had resection of the colon or rectum for cancer have been audited prospectively.

METHODS

Clinical and pathological data were collected prospectively as part of the ongoing Concord Hospital colorectal cancer project. Patients were followed up for a median of 29 months.

RESULTS

In 57 of 66 patients in whom laparoscopic resection was attempted the operation was completed laparoscopically. Three patients died from perioperative myocardial infarction. The median postoperative stay was 14 days. There was a high incidence of postoperative respiratory and cardiac complications. One patient developed a port-site metastasis.

CONCLUSION

There was no obvious benefit from laparoscopically-assisted resection of large bowel cancer in these patients.

The clinical and radiological features of cholecystocolic fistulae

The clinical and radiological features of seven patients presenting with cholecystocolic fistulae are reviewed. The majority of the patients were elderly (age range 43-85 years, mean 70.7 years) and there was a female preponderance (6:1). The condition usually has a benign clinical course. Diarrhoea was the most common presenting symptom and the typical clinical features of gallbladder disease were absent. Cholangitis occurred in only one patient. The time between onset of symptoms and diagnosis varied from 1 week to 2 years (mean 22 weeks). In only one patient was the diagnosis of biliary-intestinal fistula suspected on the basis of the plain abdominal radiograph (Case 5). A diagnosis of cholecystocolic fistula was established by barium enema (5 cases), endoscopic retrograde cholangiopancreatography (ERCP) (1 case) and diagnostic laparotomy (1 case). The only cause identified in this series was acute or chronic cholecystitis.

Cutaneous presentation of juvenile chronic myelogenous leukemia: a diagnostic and therapeutic dilemma

Annular, erythematous, circinate plaques were the first manifestation of juvenile chronic myelogenous leukemia (JCML) in an otherwise healthy 2.5-year-old boy who had had these lesions since 6 months of age. The lesions showed an atypical hematopoietic infiltrate on biopsy. Biopsy of a bone marrow specimen and peripheral blood smear were normal six months before leukemic transformation. At 3 years of age the boy developed splenomegaly, thrombocytopenia, and petechiae, and a bone marrow aspirate and cell marker studies were regarded as consistent with, if not diagnostic of, JCML. Four previous cases of cutaneous leukemic infiltrate associated with JCML have been published. Our patient had recurring urticarial-like plaques for two years before the initial bone marrow finding of JCML. Given the poor prognosis and progressively evolving course of JCML, it may be appropriate to consider therapy before bone marrow changes, based on the presence of the cutaneous eruption with the appropriate findings on skin biopsy and an elevated fetal hemoglobin.

[Cerebrovascular accidents. Case material based on hospital records]

Perceiving that inaccuracy of clinical records is the rule rather than the exception, the author examines the data base of the Amarante Regional Hospital with particular relevance to the patients who were hospitalized with cerebral vascular accident (CVA) in the Department of Internal Medicine during 1990, 1991 and 1992. The objective is to view the existing computerised hospital database as a source of information for future studies within the clinical field and, at the same time, to be aware of the department's casuistry and to contribute to the epidemiological understanding of the population who lives in the area of influence of this hospital. In this department, 24% of all the hospitalised patients had either a recent CVA or had already had one previously. On the whole, the disease affected both sexes in an equal manner, but females later than males. The mortality rate was greater in patients with CVA (17%) than in those without CVA (9%) and was also greater in CVA-females (19%) than in CVA-males (15%). The intercurrences in the community were the cause of admission in 26% of the hospitalised patients with a CVA, and were mainly respiratory, metabolic and urinary diseases, and appeared to be more serious in males. The mortality rate in patients with intercurrences (19%) was only exceeded by that caused by hemorragic accidents (22%). The author examines and discusses the instances of error during the construction and data gathering of the database and draws his own conclusions.

Hernia uteri (correction of: uterus) inguinale associated with unilateral renal agenesis

We report a patient with a rudimentary uterine horn, fallopian tube and ovary in an inguinal hernia. Associated with this abnormality the patient had ipsilateral renal agenesis and a unicornuate uterus.

Psychological assessment of postdisaster class action and personal injury litigants: a case study

The case study method is used to describe psychological assessments undertaken with victims of a combined natural/technological disaster for litigation purposes. A class action suit was filed in which the authors determined levels of traumatic stress in 27 plaintiffs as a group and relative to each other. The process was effective--the case was settled out of court in favor of the litigants. Individual litigants were satisfied with monetary awards received.

Glycogen storage disease in adults

OBJECTIVE

To identify complications amenable to prevention in adults with glycogen storage disease (GSD) types Ia, Ib, and III and to determine the effect of the disease on social factors.

DESIGN

Case series and clinical review.

SETTING

Referral medical centers in the United States and Canada.

PATIENTS

All patients with GSD-Ia (37 patients), GSD-Ib (5 patients), and GSD-III (9 patients) who were 18 years of age or older.

MEASUREMENTS

Ultrasound or radiographic studies identified liver adenomas, nephrocalcinosis, or kidney stones. Radiographic studies identified osteopenia. Reports of the clinical examination, serum chemistry results, and social data were obtained.

RESULTS

For patients with GSD-Ia, problems included short stature (90%), hepatomegaly (100%), hepatic adenomas (75%), anemia (81%), proteinuria or microalbuminuria (67%), kidney calcifications (65%), osteopenia or fractures or both (27%), increased alkaline phosphatase (61%) and gamma-glutamyltransferase (93%) activities, and increased serum cholesterol (76%) and triglyceride (100%) levels. Hyperuricemia was frequent (89%). Patients with GSD-Ib had severe recurrent bacterial infections and gingivitis. In patients with GSD-III, 67% (6 of 9) had increased creatinine kinase activity. Four of these patients had myopathy and cardiomyopathy.

CONCLUSIONS

For GSD-Ia, hyperuricemia and pyelonephritis should be treated to prevent nephrocalcinosis and additional renal damage. For GSD-Ib, granulocyte-colony-stimulating factor may prevent bacterial infections. For GSD-III, more data are required to determine whether the myopathy and cardiomyopathy can be prevented. Most of the patients with GSD-I and GSD-III had 12 or more years of education and were either currently in school or employed.

Femoral nerve palsy following laparoscopic inguinal herniorrhaphy

Laparoscopic inguinal herniorrhaphy has undergone a rapid evolution. The technique currently favored by many laparoscopic surgeons places a prosthetic mesh over the myopectineal orifice. We describe a femoral nerve palsy after such an operation and detail the anatomy of the nerves at risk during laparoscopic inguinal herniorrhaphy. We discuss how injury to these structures and the attendant anterior thigh pain and weakness may be avoided.

Radiology of starch granulomatous peritonitis

Starch granulomatous peritonitis (SGP) is a rare complication of abdominal surgery that results, in a susceptible individual, from contamination of the peritoneal cavity with starch particles from the surgeon's gloves. It is important to make the diagnosis of SGP without recourse to re-operation as the optimal treatment is non-surgical. A case of SGP that was confirmed only after re-operation and resection of the involved tissues is reported. The first description of an abdominal computed tomography scan in this condition is presented, the significance of which was only recognized postoperatively.