Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Monoclinic polymorph of Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe(anhydrous). Parallel packing of 3(10)-/alpha-helices and a transition of helix type

The structures of two crystal forms of Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe have been determined. The triclinic form (P1, Z = 1) from DMSO/H2O crystallizes as a dihydrate (Karle, Sukumar & Balaram (1986) Proc, Natl, Acad. Sci. USA 83, 9284-9288). The monoclinic form (P2(1), Z = 2) crystallized from dioxane is anhydrous. The conformation of the peptide is essentially the same in both crystal system, but small changes in conformational angles are associated with a shift of the helix from a predominantly alpha-type to a predominantly 3(10)-type. The r.m.s. deviation of 33 atoms in the backbone and C beta positions of residues 2-8 is only 0.29 A between molecules in the two polymorphs. In both space groups, the helical molecules pack in a parallel fashion, rather than antiparallel. The only intermolecular hydrogen bonding is head-to-tail between helices. There are no lateral hydrogen bonds. In the P2(1) cell, a = 9.422(2) A, b = 36.392(11) A, c = 10.548(2) A, beta = 111.31(2) degrees and V = 3369.3 A for 2 molecules of C60H97N11O13 per cell.

Aggregation studies in crystals of apolar helical peptides: Boc-Aib-Val-Ala-Leu-Aib-Val-Ala-Leu-Aib-OMe

In the crystal, the backbone of Boc-(Aib-Val-Ala-Leu)2-Aib-OMe adopts a helical form with four alpha-type hydrogen bonds in the middle, flanked by 3(10)-type hydrogen bonds at either end. The helical molecules stack in columns with head-to-tail hydrogen bonds, either directly between NH and CO, or bridged by solvent molecules. The packing of the helices is parallel, even in space group P2(1). Cell parameters are a = 9.837(2) A, b = 15.565(3) A, c = 20.087(5) A, beta = 96.42(2) degrees, dcalc = 1.091 g/cm3 for C46H83N9O12.1.5H2O.0.67CH3OH. There appears to be some hydration of the backbone in this apolar helix.

Cystine peptides Antiparallel β-sheet conformation of the cyclic biscystine peptide [Boc-Cys-Ala-Cys-NHCH3]2

The crystal structure analysis of the cyclic biscystine peptide [Boc-Cys1-Ala2-Cys3-NHCH3]2 with two disulfide bridges confirms the antiparallel ?-sheet conformation for the molecule as proposed for the conformation in solution. The molecule has exact twofold rotation symmetry. The 22-membered ring contains two transannular NH ? OC hydrogen bonds and two additional NH ? OC bonds are formed at both ends of the molecule between the terminal (CH3)3COCO and NHCH3 groups. The antiparallel peptide strands are distorted from a regularly pleated sheet, caused mainly by the L-Ala residue in which ?=� 155° and ?= 162°. In the disulfide bridge C? (1)-C? (1)-S(1)-(3')-C?(3')-C?(3'), S�S = 2.030 Å, angles C? SS = 107° and 105°, and the torsional angles are �49, �104, +99, �81, �61°, respectively. The biscystine peptide crystallizes in space group C2 with a = 14.555(2) Ã…, b = 10.854(2) Ã…, c = 16.512(2)Ã…, and ?= 101.34(1) with one-half formula unit of C30H52N8O10S4· 2(CH3)2SO per asymmetric unit. Least-squares refinement of 1375 reflections observed with |F| > 3?(F) yielded an R factor of 7.2%.

Parallel and antiparallel aggregation of alpha-helices. Crystal structures of two apolar decapeptides X-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe (X = Boc, Ac)

An apolar helical decapeptide with different end groups, Boc- or Ac-, crystallizes in a completely parallel fashion for the Boc-analog and in an antiparallel fashion for the Ac-analog. In both crystals, the packing motif consists of rows of parallel molecules. In the Boc-crystals, adjacent rows assemble with the helix axes pointed in the same direction. In the Ac-crystals, adjacent rows assemble with the helix axes pointed in opposite directions. The conformations of the molecules in both crystals are quite similar, predominantly alpha-helical, except for the tryptophanyl side chain where chi 1 congruent to 60 degrees in the Boc- analog and congruent to 180 degrees in the Ac-analog. As a result, there is one lateral hydrogen bond between helices, N(1 epsilon)...O(7), in the Ac-analog. The structures do not provide a ready rationalization of packing preference in terms of side-chain interactions and do not support a major role for helix dipole interactions in determining helix orientation in crystals. The crystal parameters are as follow. Boc-analog: C60H97N11O13.C3H7OH, space group Pl with a = 10.250(3) A, b = 12.451(4) A, c = 15.077(6) A, alpha = 96.55(3) degrees, beta = 92.31(3) degrees, gamma = 106.37(3) degrees, Z = 1, R = 5.5% for 5581 data ([F] greater than 3.0 sigma(F)), resolution 0.89 A. Ac-analog: C57H91N11O12, space group P2(1) with a = 9.965(1) A, b = 19.707(3) A, c = 16.648(3) A, beta = 94.08(1), Z = 2, R = 7.2% for 2530 data ([F] greater than 3.0 sigma(F)), resolution 1.00 A.

Modular design of synthetic protein mimics. Crystal structures, assembly, and hydration of two 15- and 16-residue apolar, leucyl-rich helical peptides

Two IS- and 16-residue peptides containing a-aminoisobutyric acid (Aib) have been synthesized, as part of a strategy to construct stereochemically rigid peptide helices, in a modular approach to design of protein mimics. The peptides Boc-(Val-Ala-Leu-Aib),-OMe ( I ) and Boc-Val-Ala-Leu-Aib-Val-Ala-Leu-(Val-Ala-Leu-Aib()11z)- OhaMvee been crystallized.Both crystals are stable only in the presence of mother liquor or water. The crystal data are as follows. I: C78H140N16019~2H20,P2,, a = 16.391 (3) A, b = 16.860 (3) A, c = 18.428 (3) A, p = 103.02 (I)O, Z = 2, R = 9.6% for 3445 data with lFol >30(F), resolution 0.93 A. 11: C7,Hl,,N,S018.7.5H,0, C2221, a = 18.348 ( 5 ) A, b = 47.382 (1 1) A, c = 24.157 ( 5 ) A, Z =8, R = l0,6%, for 3147 data with lFol > 3a(F), resolution 1.00 A. The 15-residue peptide (11) is entirely a helical, while the 16-residue peptide ( I ) has a short segment of 310 helix at the N terminus. The packing of the helices in the crystals is rather incfficicnt with no particular attractions between Leu-Leu side chains, or any other pair. Both crystals have fairly large voids, which are filled with water molecules in a disordered fashion. Water molecule sites near the polar head-to-tail regions are well detcrmined, those closer to the hydrophobic side chains less so and a number of possible water sites in the remaining "empty" space are not determined. No interdigitation of Leu side chains is observed in the crystal as is hypothesized in the "leucine zipper" class of DNA binding proteins.

Modular design of synthetic protein mimics. Crystal structure of two seven-residue helical peptide segments linked by .epsilon.-aminocaproic acid

Two seven-residue helical segments, Val-Ala-Leu-Aib-Val-Ala-Leu, were linked synthetically with an epsilon-aminocaproic acid (Acp) linker with the intention of making a stable antiparallel helix-helix motif. The crystal structure of the linked peptide Boc-Val-Ala-Leu-Aib-Val-Ala-Leu-Acp-Val-Ala-Leu-Aib-Val-Ala-Leu-OMe (1) shows the two helices displaced laterally from each other by the linker, but the linker has not folded the molecule into a close-packed antiparallel conformation. Two strong intermolecular NH...O = C hydrogen bonds are formed between the top of the lower helix of one molecule and the bottom of the upper helix in a laterally adjacent molecule to give the appearance of an extended single helix. The composite peptide with Boc and OMe end groups, C76H137N15O18.H2O, crystallize in space group P2(1) with a = 8.802 (1) angstrom, b = 20.409 (4) angstrom, c = 26.315 (3) angstrom, and beta = 90.72 (1)degrees; overall agreement R = 7.86% for 5030 observed reflections (\F(o)\ > 3-sigma(F)); resolution = 0.93 angstrom. Limited evidence for a more compact conformation in solution consistent with an antiparallel helix arrangement is obtained by comparison of the HPLC retention times and CD spectra of peptide 1 with well-characterized continuous helices of similar length and sequence.

Zervamicins, a structurally characterised peptide model for membrane ion channels

Voltage dependent membrane channels are formed by the zervamicins, a group of α-aminoisobutyric acid containing peptides. The role of polar residues like Thr, Gln and Hyp in promoting helical bundle formation is established by dramatically reduced channel lifetimes for a synthetic apolar analog. Crystal structures of Leu1-zervamicin reveal association of bent helices. Polar contacts between convex faces result in an ‘hour glass’ like arrangement of an aqueous channel with a central constriction. The structure suggests that gating mechanisms may involve movement of the Gln11 carboxamide group. Gln3 may play a role in modulating the size of the channel mouth.

Peptide mimics for structural features in proteins. Crystal structures of three heptapeptide helices with a C-terminal 6-->1 hydrogen bond.

The crystal structure determination of three heptapeptides containing alpha-aminoisobutyryl (Aib) residues as a means of helix stabilization provides a high-resolution characterization of 6-->1 hydrogen-bonded conformations, reminiscent of helix-terminating structural features in proteins. The crystal parameters for the three peptides, Boc-Val-Aib-X-Aib-Ala-Aib-Y-OMe, where X and Y are Phe, Leu (I), Leu, Phe (II) and Leu, Leu (III) are: (I) space group P1, Z = 1, a = 9.903 A, b = 10.709 A, c = 11.969 A, alpha = 102.94 degrees, beta = 103.41 degrees, gamma = 92.72 degrees, R = 4.55%; (II) space group P21, Z = 2, a = 10.052 A, b = 17.653 A, c = 13.510 A, beta = 108.45 degrees, R = 4.49%; (III) space group P1, Z = 2 (two independent molecules IIIa and IIIb in the asymmetric unit), a = 10.833 A, b = 13.850 A, c = 16.928 A, alpha = 99.77 degrees, beta = 105.90 degrees, gamma = 90.64 degrees, R = 8.54%. In all cases the helices form 3(10)/alpha-helical (or 3(10)helical) structures, with helical columns formed by head-to-tail hydrogen bonding. The helices assemble in an all-parallel motif in crystals I and III and in an antiparallel motif in II. In the four crystallographically characterized molecules, I, II, IIIa and IIIb, Aib(6) adopts a left-handed helical (hL) conformation with positive phi, psi values, resulting in 6-->1 hydrogen-bond formation between Aib(2) CO and Leu(7)/Phe(7) NH groups. In addition a 4-->1 hydrogen bond is seen between Aib(3) CO and Aib(6) NH groups. This pattern of hydrogen bonding is often observed at the C-terminus of helices proteins, with the terminal pi-type turn being formed by four residues adopting the hRhRhRhL conformation.

Conformation of the flexible bent helix of Leu1-zervamicin in crystal C and a possible gating action for ion passage

The membrane channel-forming polypeptide, Leu(1)-zervamicin, Ac-Leu-Ile-Gln-Iva-Ile(5)-Thr-Aib-Leu-Aib-Hyp(10) -Gln-Aib-Hyp-Aib-Pro(15)-Phol (Aib: alpha-aminoisobutyric acid; Iva: isovaline; Hyp: 4-hydroxyproline; Phol: phenylalininol) has been analyzed by x-ray diffraction in a third crystal form. Although the bent helix is quite similar to the conformations found in crystals A and B, the amount of bending is more severe with a bending angle approximate to 47 degrees, The water channel formed by the convex polar faces of neighboring helices is larger at the mouth than in crystals A and B, and the water sites have become disordered. The channel is interrupted in the middle by a hydrogen bond between the OH of Hyp(10) and the NH2 of the Gln(11) of a neighboring molecule. The side chain of Gln(11) is wrapped around the helix backbone in an unusual fashion in order that it can augment the polar side of the helix. In the present crystal C there appears to be an additional conformation for the Gln(11) side chain (with approximate to 20% occupancy) that opens the channel for possible ion passage. Structure parameters for C85H140N18O22.xH(2)O.C2H5OH are space group P2(1)2(1)2(1), a = 10.337 (2) Angstrom, b = 28.387 (7) Angstrom, c = 39.864 (11) Angstrom, Z = 4, agreement factor R = 12.99% for 3250 data observed > 3 sigma(F), resolution = 1.2 Angstrom. (C) 1994 John Wiley & Sons, Inc.

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.

Temperature dependence of g values in tetragonal ionic Cu++ salts

A temperature dependence has been observed in the spin-Hamiltonian parameters of the Cu++ ion in a tetragonal crystal field and the variation has been interpreted in terms of vibronic effects.

ESR and optical absorption studies in copper diethyldithiocarbamate

ESR investigations at X band and optical-absorption measurements have been reported in single crystals of copper (n) diethyldithiocarbamate Cu[S 2CN(C2H5)2]2 diluted to 0.2% with the corresponding zinc complex. The measurements have been made both at room and liquid-oxygen temperatures. ESR measurements gave the following values for the parameters in spin Hamiltonian g11=2.1085, g=2.023(6), A63= 142.4×10-4 cm-1, A65 = 152.0×10-4 cm-1, B = 22.4×10-4 cm-1, Q~3×10-4 cm-1. Polarized optical absorption study has made possible a proper assignment of the absorption bands to their corresponding transitions. This has led to information regarding the ordering of the MO levels of the complex. The coefficients used in the MO description of the complex have been calculated from the observed parameters. The results show that the metal ligand BIσ bond is purely covalent and that the out-of-plane w bonding is appreciably covalent whereas the in-plane Π bonding is ionic. Further, it is noted that the metal ligand binding is more covalent with sulfur as ligand than with oxygen or nitrogen.