Multifractality Meets Entanglement: Relation for Nonergodic Extended States.

In this work, we establish a relation between entanglement entropy and fractal dimension D of generic many-body wave functions, by generalizing the result of Page [Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291] to the case of sparse random pure states (SRPS). These SRPS living in a Hilbert space of size N are defined as normalized vectors with only N^{D} (0≤D≤1) random nonzero elements. For D=1, these states used by Page represent ergodic states at an infinite temperature. However, for 01 and to genuine multifractal states and also show that their fluctuations have ergodic behavior in a narrower vicinity of the ergodic state D=1.

Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems.

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling the time evolution as cellular automata for specific cases of dipole- and quadrupole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher-moment conservation.

Characterizing Time Irreversibility in Disordered Fermionic Systems by the Effect of Local Perturbations.

We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time irreversibility. We focus on three different systems: the noninteracting Anderson and Aubry-André-Harper (AAH) models and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave functions by measuring the Loschmidt echo (LE). We show that in the extended or ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the long-time limit, in contrast to the noninteracting localized phase where some memory is always preserved.

Density Propagator for Many-Body Localization: Finite-Size Effects, Transient Subdiffusion, and Exponential Decay.

We investigate charge relaxation in quantum wires of spinless disordered fermions (t-V model). Our observable is the time-dependent density propagator Π_{ϵ}(x,t), calculated in windows of different energy density ϵ of the many-body Hamiltonian and at different disorder strengths W, not exceeding the critical value W_{c}. The width Δx_{ϵ}(t) of Π_{ϵ}(x,t) exhibits a behavior dlnΔx_{ϵ}(t)/dlnt=ß_{ϵ}(t), where the exponent function ß_{ϵ}(t)≲1/2 is seen to depend strongly on L at all investigated parameter combinations. (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that ß_{ϵ}(t)<1/2 in a large window of times. However, subdiffusion might possibly be transient, only, finally giving way to a conventional diffusive behavior with ß_{ϵ}=1/2. (ii) We cannot confirm the existence of many-body mobility edges even in regions of the phase diagram that have been reported to be deep in the delocalized phase. (iii) (Transient) subdiffusion 0<ß_{ϵ}(t)≲1/2 coexists with an enhanced probability for returning to the origin Π_{ϵ}(0,t), decaying much slower than 1/Δx_{ϵ}(t). Correspondingly, the spatial decay of Π_{ϵ}(x,t) is far from Gaussian, being exponential or even slower. On a phenomenological level, our findings are broadly consistent with the effects of strong disorder and (fractal) Griffiths regions.

Quantum Mutual Information as a Probe for Many-Body Localization.

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

Treatment of Uterine Myoma with 2.5 or 5 mg Mifepristone Daily during 3 Months with 9 Months Posttreatment Followup: Randomized Clinical Trial.

Objectives. To evaluate the efficacy, safety, and quality of life by using 2.5 and mifepristone 5 mg daily doses to treat uterine fibroids over 3 months with a 9-month followup period. Design. Randomized clinical trial. Place. "Eusebio Hernández" Hospital, Havana, Cuba. Subjects. 220 women with symptomatic uterine fibroids. Treatment. One-half (2.5 mg) or one-whole 5 mg mifepristone tablet. Variables to Evaluate Efficacy. Changes in fibroid and uterine volumes, in symptomatic prevalence and intensity, and in quality of life. Results. After 3-month treatment, fibroid volume decreased by 27.9% (CI 95% 20-35) and 45.5% (CI 95% 37-62), in the 2.5 and 5 mg groups, respectively, P = 0.003. There was no difference in the prevalence of symptoms at the end of treatment, unlike after 6- and 9-month followup when there was a difference. Amenorrhea was significantly higher in the 5 mg group, P = 0.001. There were no significant differences in mifepristone side effects between the groups. Both groups displayed a similar improvement in quality of life. Conclusions. The 2.5 mg dosage resulted in a lesser reduction in fibroid size but a similar improvement in quality of life when compared to the 5 mg dose. This trial is registered with ClinicalTrials.gov NCT01786226.

Mifepristone versus placebo to treat uterine myoma: a double-blind, randomized clinical trial.

OBJECTIVE: To evaluate the efficacy, safety, and quality of life of 5 mg mifepristone per day compared with a placebo in treating uterine fibroids. DESIGN: Randomized, double-blind clinical study. LOCATION: Eusebio Hernández Gynecology and Obstetrics Teaching Hospital, Havana, Cuba. SUBJECTS: One hundred twenty-four subjects with symptomatic uterine fibroids. TREATMENT: One daily capsule of 5 mg mifepristone or a mifepristone placebo over 3 months. VARIABLES IN EVALUATING SAFETY: Changes in fibroid and uterine volumes, changes in symptom prevalence and intensity, and changes in quality of life. RESULTS: Three months into treatment, fibroid volume was reduced by 28.5% in the mifepristone group with an increase of 1.8% in the placebo group (P = 0.031). There were significant differences between the groups with respect to pelvic pain prevalence (P = 0.006), pelvic pressure (P = 0.027), rectal pain (P = 0.013), hypermenorrhea (P < 0.001), and metrorrhagia (P = 0.002) at the end of treatment. Amenorrhea was 93.1% and 4.3% in the mifepristone and placebo groups, respectively (P < 0.001). Treatment side effects were significantly greater in the mifepristone group. Estradiol levels did not differ significantly between the placebo and mifepristone groups at the end of treatment. Improvement in quality of life was significantly greater in the categories of "symptoms" (P = 0.004) and "activity" (P = 0.045) in the mifepristone group. CONCLUSION: The 5 mg dosage of mifepristone presented significantly superior efficacy compared to the placebo.

Safety and effectiveness of different dosage of mifepristone for the treatment of uterine fibroids: a double-blind randomized clinical trial.

OBJECTIVES: The aim of this study was to evaluate the safety and improvement in quality of life using 10 mg and 5 mg daily doses of mifepristone for the treatment of uterine fibroids. DESIGN: The research was a randomized double-blind clinical study undertaken at the Eusebio Hernández Hospital in Havana, Cuba. SUBJECTS AND METHODS: Seventy subjects with symptomatic uterine fibroids took one daily capsule of 10 mg or 5 mg mifepristone orally for 9 months. One to three endometrial biopsies were performed. In evaluating safety, the variables studied were endometrial changes associated with mifepristone, elevation of hepatic transaminases, side effects of mifepristone, and instances and duration of irregular bleeding. RESULTS: There were 30/49 (61.2%) and 13/24 (54.2%) diagnoses of endometrial changes associated with mifepristone in the 10 mg and 5 mg groups, respectively (P = 0.282). At every evaluation visit the average endometrial thickness was significantly greater in the 10 mg group than in the 5 mg group (P = 0.013, P = 0.002, and P = 0.013, respectively). Only five subjects had slight elevations in their hepatic transaminases after 9 months' treatment. Sixteen of 35 (45.7%) and eight of 33 (24.2%) subjects had the occasional hot flush in the 10 mg and 5 mg groups, respectively (P = 0.032). In total, there were 12.9 ± 4.6 (n = 21) and 9.1 ± 3.9 (n = 18) days of irregular bleeding in the 10 mg and 5 mg groups, respectively (P = 0.009). CONCLUSION: According to the study findings, a 5 mg daily dose over 9 months has a relatively better safety profile than the 10 mg dose.

Mifepristone 2.5 mg versus 5 mg daily in the treatment of leiomyoma before surgery.

OBJECTIVES: To evaluate the efficacy and safety of 2.5 mg and 5 mg mifepristone during 3 months for the treatment of uterine fibroids before surgery. DESIGN: Multicenter randomized clinical trial. LOCATIONS: Eusebio Hernández Hospital, Havana, Cuba and the Alemán Hospital, Managua, Nicaragua. SUBJECTS: Included in the study were 146 women with symptomatic uterine fibroids. TREATMENT: GROUP I: half a tablet of 5 mg (2.5 mg) mifepristone taken orally every 24 hours, and Group II: one tablet of 5 mg mifepristone taken orally every 24 hours over a period of 3 months in both groups. Two endometrial biopsies were performed. VARIABLES TO EVALUATE EFFICACY: Increase in average hemoglobin, changes in fibroid and uterine volume, and symptomatic improvement. RESULTS: The average hemoglobin at the end of treatment was 0.6 g/dL greater in the 5 mg mifepristone group (P = 0.033). In both groups there were similar reductions in fibroid volumes. Clinical improvement was more significant in the 5 mg group. CONCLUSION: The dose to be used should be 5 mg.

Tratamiento de la endometriosis con 5 mg o 25 mg diarios de mifepristona durante 6 meses. Ensayo clínico aleatorizado, doble ciego / Treatment with 5mg or 25mg of mifepristone daily for six months. A randomized double-blind study

Objetivos. Evaluar la eficacia y seguridad de 5 y 25 mg de mifepristona en el tratamiento de la endometriosis. Diseño. Ensayo clínico aleatorizado, doble ciego. Lugar. Hospital Eusebio Hernández, La Habana, Cuba. Sujetos. Veintiséis mujeres con diagnóstico laparoscópico de endometriosis. Tratamientos. Grupo I: una tableta oral diaria de 25mg de mifepristona, o grupo II: una tableta oral diaria de 5mg de mifepristona, durante 6 meses. Se realizó laparoscopia y biopsia endometrial pre y postratamiento. Variable para evaluar eficacia. Reducción de la intensidad de la dismenorrea medida por una escala visual análoga. Resultados. En ambos grupos las disminuciones de la intensidad de la dismenorrea y la dispareunia fueron muy significativas comparadas con los valores iniciales. Todas las mujeres estaban en amenorrea a los 45 días de tratamiento. Conclusiones. La mifepristona, en dosis de 25 o 5mg, podría ser una alternativa para el tratamiento de la endometriosis (AU)

Objectives. To evaluate the safety and efficacy of 5 mg and 25 mg doses of mifepristone for the treatment of endometriosis. Design. Randomized double-blind study. Setting. Eusebio Hernández Hospital, Havana, Cuba. Subjects. Twenty-six women laparoscopically diagnosed with endometriosis were included. Treatment. Group I received one tablet of 25mg mifepristone daily and group II received one tablet of 5mg mifepristone daily for 6 months. Laparoscopy and endometrial biopsy were performed before and after treatment. Variable to evaluate efficacy. Reduction in the intensity of dysmenorrhea measured by a visual analogue scale. Results. In both groups reductions in the intensity of dysmenorrhea and dyspareunia were highly significant compared with initial values (P<.001). All the women were amenorrheic after 45 days of treatment. Conclusions. At doses of 5mg or 25mg, mifepristone could be an alternative for the treatment of endometriosis (AU)

Mifepristona 5 mg frente a 10 mg diarios en el tratamiento del leiomioma. Ensayo clínico aleatorizado / 5 mg versus 10 mg mifepristone daily in the treatment of leiomyoma: A randomised clinical trial

Objetivo Evaluar la eficacia y seguridad de 5 mg o 10 mg diarios de mifepristona durante 3 meses para el tratamiento del fibroma. Material y métodos 90 mujeres con fibromatosis uterina sintomática se asignaron aleatoriamente a recibir 5 o 10mg de mifepristona (45 por grupo). Mediante ultrasonografía abdominal se calcularon los volúmenes del fibroma y del útero. La eficacia se estimó por la reducción de los volúmenes del fibroma, del útero y la prevalencia de los síntomas. Resultados El fibroma se redujo en 60,8% (p<0,001) y 59,4% (p<0,001) en los grupos de 5 y 10mg, respectivamente. Hubo disminuciones muy significativas de los síntomas del fibroma en cada grupo de tratamiento. En los grupos de 5 y 10mg estaban amenorreicas el 86,4 y el 93,0% de las mujeres, respectivamente. No hubo ninguna hiperplasia endometrial. Conclusiones Ambos tratamientos fueron eficaces en el tratamiento del mioma uterino (AU)

Objective To estimate the efficacy and safety of 5 mg or 10 mg mifepristone daily in the treatment of leiomyoma. Material and methods Ninety women with symptomatic uterine myomas were randomised to receive 5mg or 10mg of mifepristone (45 per group). Leiomyomata and uterine volumes were evaluated by ultrasonography. Efficacy was estimated by the reduction of the leiomyomata and uterine volumes and the prevalence of symptoms. Results After treatment, in the 5mg group there was a 60.8%, (P<.001), reduction in the fibroid volume and it was 59.4%, (P<.001), in the 10mg group. The prevalence of symptoms decreased significantly. After treatment, 93.8% subjects from the 10mg mifepristone group and 86.4% subjects from the 5mg group were amenorrheic, respectively. Conclusions Both treatments were effective for treating uterine fibroids (AU)

Manejo activo de la tercera fase del parto más 400 mg de misoprostol sublingual y 200 mg de misoprostol rectal frente a manejo activo solo en la prevención de la hemorragia posparto. Ensayo clínico aleatorizado / Active management of the third phase of labour plus 400 mg of sublingual misoprostol and 200 mg of rectal misoprostol versus active management only in the prevention of post-partum haemorrhage. A randomised clinical trial

Objetivos: Evaluar la eficacia y la seguridad de 400 mg de misoprostol por vía sublingual y 200 mg rectal más manejo activo de la tercera fase del parto frente a manejo activo para prevenir la hemorragia posparto. Sujetos y métodos: Se sometió a 1.400 mujeres a recibir el misoprostol más manejo activo (grupo I) o manejo activo (grupo II). Las variables medidas fueron la incidencia de hemorragia posparto, el volumen de sangre perdido y el uso de uterotónicos adicionales. Resultados: En el grupo I hubo 28/702 (4,0%) hemorragias y en el grupo II 50/698 (7,2%), p = 0,005; riesgo relativo (RR) = 0,538; intervalo de confianza (IC) del 95% para RR (0,335-0,866). En mujeres con hemorragia posparto, el volumen de sangre perdida fue 981 ± 309 cc y 888 ± 326 cc, p = 0,225 en los grupos I y II, respectivamente. Necesitaron uterotónicos adicionales 33 (4,7%) frente a 54 (7,7% mujeres, p = 0,025 en los grupos I y II, respectivamente). Conclusiones: Se podría recomendar la administración de misoprostol por vía sublingual/rectal junto al manejo activo para prevenir la hemorragia posparto (AU)

Objectives: To evaluate the efficacy and safety of 400 mg sublingual misoprostol and 200 mg rectal misoprostol plus active management of the third stage of labour versus active management only to prevent postpartum haemorrhage. Subjects and methods: A total of 1400 women were randomly assigned to receive misoprostol plus active management (group I) or active management only (group II). The variables studied were incidence of postpartum haemorrhage, blood volume lost and need of additional uterotonics. Results: In group I there were 28/702 (4.0%) haemorrhages and in group II 50/698 (7.2%), P=.005; RR =.538; 95% CI for RR (0.335-0.866). In women having postpartum haemorrhage the lost blood volume was 981 ± 309 cc and 888 ± 326 cc. P=.225 in groups I and II, respectively. Additional uterotonics were needed in 33 women in group I (4.7%) vs. 54(7.7%) women in group II (P=.025). Conclusions: The use of sublingual/rectal misoprostol plus active management appears to be useful for the prevention of postpartum haemorrhage (AU)