Entanglement entropy in de Sitter: no pure states for conformal matter

In this paper, we consider the entanglement entropy of conformal matter for finite and semi-infinite entangling regions, as well as the formation of entanglement islands in four-dimensional de Sitter spacetime partially reduced to two dimensions. We analyze complementarity and pure state condition of the entanglement entropy of pure states and show that they never hold in the given setup. We consider two different types of Cauchy surfaces in the extended static patch and flat coordinates, correspondingly. For former, we found that entanglement entropy of a pure state is always bounded from below by a constant and never becomes zero, as required by quantum mechanics. In turn, the difference between the entropies for some region and its complement, which should be zero for a pure state, in direct calculations essentially depends on how the boundaries of these regions evolve with time. Regarding the flat coordinates, it is impossible to regularize spacelike infinity in a way that would be compatible with complementarity and pure state condition, as opposed, for instance, to two-sided Schwarzschild black hole. Finally, we discuss the information paradox in de Sitter and show that the island formula does not resolve it. Namely, we give examples of a region with a time-limited growth of entanglement entropy, for which there is no island solution, and the region, for which entanglement entropy does not grow, but the island solution exists.Comment: v1: 25 pages, 10 figures; v2: 25 pages, 10 figures, references added, notation clarifie

Entanglement Islands and Infrared Anomalies in Schwarzschild Black Hole

In this paper, island formation for entangling regions of finite size in the asymptotically flat eternal Schwarzschild black hole is considered. We check the complementarity property of entanglement entropy which was implicitly assumed in previous studies for semi-infinite regions. This check reveals the emergence of infrared anomalies after regularization of a Cauchy surface. A naive infrared regularization based on ``mirror symmetry'' is considered and its failure is shown. We introduce an improved regularization that gives a correct limit agreed with the semi-infinite results from previous studies. As the time evolution goes, the endpoints of a finite region compatible with the improved regularization become separated by a timelike interval. We call this phenomenon the ``Cauchy surface breaking''. Shortly before the Cauchy surface breaking, finite size configurations generate asymmetric entanglement islands in contrast to the semi-infinite case. Depending on the size of the finite regions, qualitatively new behaviour arises, such as discontinuous evolution of the entanglement entropy and the absence of island formation. Finally, we show that the island prescription does not help us to solve the information paradox for certain finite size regions.Comment: v1: 55 pages, 19 figures; v2: 57 pages, 19 figures, references added, Sec. 5 presentation improve

Local quenches in fracton field theory: non-causal dynamics and fractal excitation patterns

We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green function, $\langle \phi^2\rangle$ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension, and argue that this phenomenon cannot be explained by a simple self-interference effect.Comment: v1: 25 pages, 7 figures; v2: 25 pages, 7 figures, references added, minor correction

Robust bifunctional aluminium-salen catalysts for the preparation of cyclic carbonates from carbon dioxide and epoxides

Abstract Two new one-component aluminium-based catalysts for the reaction between epoxides and carbon dioxide have been prepared. The catalysts are composed of aluminium-salen chloride complexes with trialkylammonium groups directly attached to the aromatic rings of the salen ligand. With terminal epoxides, the catalysts induced the formation of cyclic carbonates under mild reaction conditions (25-35 °C; 1-10 bar carbon dioxide pressure). However, with cyclohexene oxide under the same reaction conditions, the same catalysts induced the formation of polycarbonate. The catalysts could be recovered from the reaction mixture and reused. 161

Historic Light Curve and Long-term Optical Variation of BL Lacertae 2200+420

In this paper, historical optical(UBVRI) data and newly observed data from the Yunnan Observatory of China(about100 years) are presented for BL Lacertae. Maximum variations in UBVRI: 5.12, 5.31, 4.73, 2.59, and 2.54 and color indices of U-B = -0.11 +/- 0.20, B-V= 1.0 +/- 0.11, V-R= 0.73 +/- 0.19, V-I= 1.42 +/- 0.25, R-I= 0.82 +/- 0.11, and B-I= 2.44 +/- 0.29 have been obtained from the literature; The Jurkevich method is used to investigate the existence of periods in the B band light curve, and a long-term period of 14 years is found. The 0.6 and 0.88 year periods reported by Webb et al.(1988) are confirmed. In addition, a close relation between B-I and B is found, suggesting that the spectra flattens when the source brightens.Comment: 21 pages, 6 figures, 2 table, aasms4.sty, to be published in ApJ, Vol. 507, 199

Curie Temperatures for Three-Dimensional Binary Ising Ferromagnets

Using the Swendsen and Wang algorithm, high accuracy Monte Carlo simulations were performed to study the concentration dependence of the Curie temperature in binary, ferromagnetic Ising systems on the simple-cubic lattice. Our results are in good agreement with known mean-field like approaches. Based on former theoretical formulas we propose a new way of estimating the Curie temperature of these systems.Comment: nr. of pages:13, LATEX. Version 2.09, Scientific Report :02/1994 (Univ. of Bergen, Norway), 7 figures upon reques

Experimental study of negative photoconductivity in n-PbTe(Ga) epitaxial films

We report on low-temperature photoconductivity (PC) in n-PbTe(Ga) epitaxial films prepared by the hot-wall technique on -BaF_2 substrates. Variation of the substrate temperature allowed us to change the resistivity of the films from 10^8 down to 10_{-2} Ohm x cm at 4.2 K. The resistivity reduction is associated with a slight excess of Ga concentration, disturbing the Fermi level pinning within the energy gap of n-PbTe(Ga). PC has been measured under continuous and pulse illumination in the temperature range 4.2-300 K. For films of low resistivity, the photoresponse is composed of negative and positive parts. Recombination processes for both effects are characterized by nonexponential kinetics depending on the illumination pulse duration and intensity. Analysis of the PC transient proves that the negative photoconductivity cannot be explained in terms of nonequilibrium charge carriers spatial separation of due to band modulation. Experimental results are interpreted assuming the mixed valence of Ga in lead telluride and the formation of centers with a negative correlation energy. Specifics of the PC process is determined by the energy levels attributed to donor Ga III, acceptor Ga I, and neutral Ga II states with respect to the crystal surrounding. The energy level corresponding to the metastable state Ga II is supposed to occur above the conduction band bottom, providing fast recombination rates for the negative PC. The superposition of negative and positive PC is considered to be dependent on the ratio of the densities of states corresponding to the donor and acceptor impurity centers.Comment: 7 pages, 4 figure

Влияние замещения алюминием на поле эффективной магнитной анизотропии и степень магнитной текстуры анизотропных поликристаллических гексагональных ферритов бария и стронция для подложек микрополосковых приборов СВЧ–электроники

Abstract. In this paper, the effect of Al3+ ions substitutions on the value of the effective magnetic anisotropy field НАeff and the degree of magnetic texture f of the anisotropic polycrystalline hexagonal barium and strontium ferrites were studied. The samples were obtained by the ceramic technology method and the texture was formed by pressing in a magnetic field. The sample preparation technology presented in detail. The batches of barium hexaferrites were synthesized with the concentration of Al3+ ions: 0.9; 1.4; 2.5 and 2.6 formula units while strontium hexaferrites had Al3+ concentration of 0.1 formula units. It has been shown that by this technology barium and strontium hexaferrites with high value of (in range of 19—35 kOe) and with f = 80—83% could be obtained. The achieved values of НАeff and f could be sufficient for the production of substrates for microstrip microwave devices in millimeter−wave region.For the first time a raise in the degree of magnetic texture of polycrystalline barium hexaferrites with an increase of concentration of Al3+ ions were detected; a slight (5.5—5.8%) magnetic texture of isotropic strontium hexaferrites was also detected. The achieved results discussed in detail. For studied hexaferrites the mechanism of magnetic texture formation during the process of synthesis is proposed.Аннотация. Изучено влияние замещения ионами Al3+ на величину поля эффективной магнитной анизотропии НАэфф и степень магнитной текстуры f анизотропных поликристаллических гексагональных ферритов бария и стронция. Партии образцов получены методом керамической технологии, текстура сформирована путем прессования в магнитном поле. Детально представлена технология получения объектов исследования. Синтезированы партии гексаферритов бария с концентрацией ионов Al3+ 0,9, 1,4, 2,5 и 2,6 форм. ед. и партии гексаферритов стронция с концентрацией 0,1 форм. ед. Показано, что используемая технология позволяет получать гексаферриты бария и стронция со значениями НАэфф = 19÷35 кЭ и f = 80÷83 %. Указанных значений НАэфф и f может быть вполне достаточно для производства подложек для микрополосковых СВЧ−приборов миллиметрового диапазона длин волн. Впервые обнаружен рост степени магнитной текстуры поликристаллических гексаферритов бария с ростом концентрации ионов Al3+; также обнаружена незначительная магнитная текстура 5,5—5,8 % в изотропных стронциевых гексаферритах. Представлены объяснения полученных результатов. Предложен механизм формирования магнитной текстуры в исследованных гексаферритах в процессе синтеза

Измерение поля эффективной магнитной анизотропии и ширины линии ферромагнитного резонанса на частоте ФМР в магнитноодноосных гексагональных ферритах

The work is purely metrological in nature. The developed methods for measuring the effective magnetic anisotropy field HAeff and the line width of ferromagnetic resonance ∆H of magnetically-axis hexagonal ferrites in the working frequency range of the microwave range of electromagnetic waves are presented. Methods allow to determine HAeff in the ranges of 10—23 kOe and 28—40 kOe and ΔН in the range of 0.5÷5 kOe. The first technique (measurement technique in free space in the three-millimeter wavelength range) is implemented in the frequency range 78.33—118.1 GHz. The second technique (the technique using the microstrip transmission line) is implemented in the frequency range from 25 to 67 GHz.Testing of the methods on polycrystalline samples of hexagonal barium and strontium ferrites (both nominal composition and complex ones) with a high degree of magnetic texture, comparison of measurement results with results obtained using standard measurement techniques on spherical samples showed their high accuracy and reliability.Рассмотрены вопросы метрологии и определения магнитных величин. Представлены разработанные методики измерения поля эффективной магнитной анизотропии НАэфф и ширины линии ферромагнитного резонанса ∆Н магнитноодноосных гексагональных ферритов в рабочем диапазоне частот СВЧ-диапазона электромагнитных волн. Методики позволяют определить НАэфф в диапазонах 10—23 и 28—40 кЭ и ∆Н в диапазоне 0,5—5,0 кЭ. Первая методика (методика измерения в свободном пространстве в трехмиллиметровом диапазоне длин волн) реализована в диапазоне частот 78,33—118,1 ГГц. Вторая методика (методика с использованием микрополосковой линии передачи) — в диапазоне частот от 25 до 67 ГГц.Апробация методик на поликристаллических образцах гексагональных ферритов бария и стронция (как номинального состава, так и сложнозамещенных) с высокой степенью магнитной текстуры, а также сравнение результатов измерений с результатами, полученными с применением общепринятых методик измерений на сферических образцах, показали высокую точность и надежность разработанных методик