Adiabatic Deformation Research Articles

Strain‐ and torsion‐induced resonance energy tuning of Raman scattering in single‐wall carbon nanotubes

AbstractRaman excitation profiles for homogeneously deformed single‐walled carbon nanotubes are calculated and systematically analyzed. A number of attractive and apparent effects significant in designing electromechanical devices are caused by torsion and uniaxial strain. The shift of radial breathing mode (RBM) phonon energies due to deformation is negligible. The linear dependence of electronic transition energy shift on deformation is confirmed and it is found that the slope of it is strongly related to the chiral angle of the tube. It is also shown that for some tubes the transition energy shift covers the entire visible‐light interval, making them perfectly tunable light absorbers. Two types of deformation are compared, a relaxed (slow) deformation and an adiabatic (fast) one. It is found that transition energies are more sensitive to adiabatic deformation, which can be useful for optomechanical device designing.Raman excitation profile of a (9,9) nanotube under torsion.

Formation of adiabatic shear band and deformation mechanisms during warm compression of Ti–6Al–4V alloy

Adiabatic shear band (ASB) was narrow region where softening occurred and concentrated plastic deformation took place. In present study, the effects of height reduction and deformation temperature on ASB were investigated by means of optical microscopy (OM) and scanning electron microscopy (SEM). And the deformation mechanisms within the shear band were discussed thoroughly with the help of transmission electron microscopy (TEM). There is a critical strain for the formation of ASB during warm compression of Ti–6Al–4V alloy. The width of ASB increases with height reduction increasing. Elongated alpha grains within shear band grow up with deformation temperature increasing. Some ultrafine grains that confirm the occurrence of dynamic recrystallization are observed within shear band during warm compression of Ti–6Al–4V alloy. There is a critical strain for the formation of adiabatic shear band during warm compression of Ti–6Al–4V alloy. Some ultrafine grains within shear band are observed during warm compression of Ti–6Al–4V alloy; it confirms the occurrence of dynamic recrystallization of α phase.

Diffusive transformation at high strain rate: On instantaneous dissolution of precipitates in aluminum alloy during adiabatic shear deformation

Abstract

Comparison of Experimental Results with Numerical Solution of Thermal Stress Analysis

This paper presents experimental measurement of the first stress invariant on the plate with hole at fatigue testing machine due to adiabatic elastic deformation. The theoretical part is concentrated on the theory of thermal stress analysis focusing on thermoelastic analysis. The experimental part is dedicated to the postprocessing of the measured data including analytical and numerical solutions for the plate with hole using finite element method (FEM).

Geometric Adiabatic Transport in Quantum Hall States.

We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.

Adiabatic topological quantum computing

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.

Symmetry-protected topological order in magnetization plateau states of quantum spin chains

A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization plateau states of one-dimensional antiferromagnets which satisfy the conditions $S\ensuremath{-}m\ensuremath{\in}$ odd integer, where $S$ is the spin quantum number and $m$ the magnetization per site, can be identified as symmetry-protected topological states if an inversion symmetry about the link center is present. This assertion is reached by mapping the antiferromagnet into a nonlinear sigma model type effective field theory containing a novel Berry phase term (a total derivative term) with a coefficient proportional to the quantity $S\ensuremath{-}m$, and then analyzing the topological structure of the ground state wave functional which is inherited from the latter term. A boson-vortex duality transformation is employed to examine the topological stability of the ground state in the absence/presence of a perturbation violating link-center inversion symmetry. Our prediction based on field theories is verified by means of a numerical study of the entanglement spectra of actual spin chains, which we find to exhibit twofold degeneracies when the aforementioned condition is met. We complete this study with a rigorous analysis using matrix product states.

Disentangled Topological Numbers by a Purification of Entangled Mixed States for Non-Interacting Fermion Systems

We argue that the entanglement Chern number proposed recently is invariant under the adiabatic deformation of a gapped many-body groundstate into a {\it disentangled/purified} one, which implies a partition of the Chern number into subsystems (disentangled Chern number). We generalize the idea to another topological number, the Z$_2$ Berry phase for a system with particle-hole symmetry, and apply it to a groundstate in a weak topological phase where the Chern number vanishes but the groundstate nevertheless has edge states. This entanglement Berry phase is especially useful for characterizing random systems with nontrivial edge states.

Hot Workability and Processing Maps of 7150 Aluminum Alloys with Zr and V Additions

The hot workability and processing maps of 7150 aluminum alloys with different Zr additions (0-0.15 wt.%) and V additions (0.01-0.15 wt.%) were investigated using uniaxial compression tests conducted at various temperatures (300-450 °C) and strain rates (0.001-10 s−1). The results reveal that the processing map of the 7150 base alloy exhibits a single domain (Domain I) associated with dynamic recovery and partially dynamic recrystallization. With the increasing Zr and V additions, Domain I shrinks toward higher temperatures and higher strain rates and exhibits decreases in efficiency of power dissipation due to a restrained level of dynamic recovery caused by the pinning effect of Al3Zr and Al21V2 dispersoids. When the added Zr and V contents reach 0.15%, another domain (Domain II) is formed, corresponding to cavity formation in the microstructure. Flow instability during hot deformation of 7150 alloys is attributed to the formation of adiabatic shear bands and deformation bands. The instability region extends toward lower strain rates when alloyed with Zr and V. The optimum hot-working parameters for those alloys are determined to be a deformation temperature of 450 °C and a strain rate of 0.01 s−1.

Fault-tolerant holonomic quantum computation in surface codes

We show that universal holonomic quantum computation (HQC) can be achieved fault-tolerantly by adiabatically deforming the gapped stabilizer Hamiltonian of the surface code, where quantum information is encoded in the degenerate ground space of the system Hamiltonian. We explicitly propose procedures to perform each logical operation, including logical state initialization, logical state measurement, logical CNOT, state injection and distillation,etc. In particular, adiabatic braiding of different types of holes on the surface leads to a topologically protected, non-Abelian geometric logical CNOT. Throughout the computation, quantum information is protected from both small perturbations and low weight thermal excitations by a constant energy gap, and is independent of the system size. Also the Hamiltonian terms have weight at most four during the whole process. The effect of thermal error propagation is considered during the adiabatic code deformation. With the help of active error correction, this scheme is fault-tolerant, in the sense that the computation time can be arbitrarily long for large enough lattice size. It is shown that the frequency of error correction and the physical resources needed can be greatly reduced by the constant energy gap.

Flow softening mechanism of Ti–5Al–2Sn–2Zr–4Mo–4Cr with different initial microstructures at elevated temperature deformation

The flow softening mechanism of Ti–5Al–2Sn–2Zr–4Mo–4Cr with different initial microstructures was investigated considering the plastic deformation heat effect and the microstructure evolution. Two initial microstructures were employed: one initial microstructure A (MA) with equiaxed and elongated primary α grains, and another initial microstructure B (MB) with Widmanstätten α platelets. The adiabatic plastic deformation effect was estimated by calculating the temperature rise, and the microstructure evolution was observed by using OM, TEM and EBSD. The results revealed that the initial microstructure B presented a higher flow softening effect at a certain deformation temperature and strain rate than the initial microstructure A. For both the two initial microstructures, the plastic deformation heat effect was one of the main factors for flow softening at the strain rates above 0.01s−1 and the dynamic recovery dominated the shape of strain–stress curves at a strain rate of 0.01s−1. The flow localization for the initial microstructure B at a strain rate of 5.0s−1 was more evident, which led to the larger flow softening effect. Moreover, the dynamic recrystallization for the initial microstructure A at the strain rates above 0.01s−1 was another main factor for flow softening, and the platelet kinking/bending for the initial microstructure B at all the deformation conditions played an important role in the flow softening, which was also responsible for the larger flow softening effect comparing with the initial microstructure A.

Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions

The adiabatic groupoid Gad of a smooth groupoid G is a deformation relating G with its algebroid. In a previous work, we constructed a natural action of R on the C*-algebra of zero order pseudodifferential operators on G and identified the crossed product with a natural ideal J(G) of C⁎(Gad). In the present paper we show that C⁎(Gad) itself is a pseudodifferential extension of this crossed product in a sense introduced by Saad Baaj. Let us point out that we prove our results in a slightly more general situation: the smooth groupoid G is assumed to act on a C*-algebra A. We construct in this generalized setting the extension of order 0 pseudodifferential operators Ψ(A,G) of the associated crossed product A⋊G. We show that R acts naturally on Ψ(A,G) and identify the crossed product of A by the action of the adiabatic groupoid Gad with an extension of the crossed product Ψ(A,G)⋊R. Note that our construction of Ψ(A,G) unifies the ones of Connes (case A=C) and of Baaj (G is a Lie group).

Description of the thermoelastic effect in solids in a wide temperature range

The change in temperature under adiabatic elastic deformation of solids (thermoelastic effect) at low and high temperatures has been calculated taking into account the quantum properties of thermal dynamics. In the high-temperature range, a quantum-mechanical correction to the classical Kelvin formula has been found. In the low-temperature range, a new formula for the description of the thermoelastic effect has been derived.

Bulk angular momentum and Hall viscosity in chiral superconductors

We establish the Berry-phase formulas for the angular momentum (AM) and the Hall viscosity (HV) to investigate chiral superconductors (SCs) in two and three dimensions. The AM is defined by the temporal integral of the anti-symmetric momentum current induced by an adiabatic deformation, while the HV is defined by the symmetric momentum current induced by the symmetric torsional electric field. Without suffering from the system size or geometry, we obtain the macroscopic AM $L_z = \hbar m N_0/2$ at zero temperature in full-gap chiral SCs, where $m$ is the magnetic quantum number and $N_0$ is the total number of electrons. We also find that the HV is equal to half the AM at zero temperature not only in full-gap chiral SCs as is well-known but also in nodal ones, but its behavior at finite temperature is different in the two cases.

Identifying non-Abelian topological ordered state and transition by momentum polarization

Using a method called momentum polarization, we study the quasiparticle topological spin and edge-state chiral central charge of non-Abelian topological ordered states described by Gutzwiller-projected wave functions. Our results verify that the fractional Chern insulator state obtained by Gutzwiller projection of two partons in bands of Chern number 2 is described by $SU(2)_2$ Chern-Simons theory coupled to fermions, rather than the pure $SU(2)_2$ Chern-Simons theory. In addition, by introducing an adiabatic deformation between one Chern number 2 band and two Chern number 1 bands, we show that the topological order in the Gutzwiller-projected state does not always agree with the expectation of topological field theory. Even if the parton mean-field state is adiabatically deformed, the Gutzwiller projection can introduce a topological phase transition between Abelian and non-Abelian topologically ordered states. Our approach applies to more general topologically ordered states described by Gutzwiller-projected wave functions.

Noncommutative static strings from matrix models

We examine the noncommutative cylinder solution to a matrix model with a Minkowski background metric. It can be regarded as the noncommutative analogue of a static circular string. Perturbations about the solution yield a tachyonic scalar field (and an additional tachyonic fermion in the full supersymmetric version of the model) in the commutative limit. The tachyonic mode is attributed to the fact that the circular string is unstable under uniform adiabatic deformations. We obtain a stabilizing term which when added to the matrix model removes the tachyonic mass.

Almost quantum adiabatic dynamics and generalized time-dependent wave operators

We consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit. To treat these systems we introduce a generalization of the time-dependent wave operator theory which is usually used to treat dynamics which do not escape too far from an initial subspace called the active space. Our generalization is based on a time-dependent adiabatic deformation of the active space. The geometric phases associated with the almost adiabatic representation are also derived. We use this formalism to study the adiabaticity of a dynamics surrounding an exceptional point of a non-Hermitian Hamiltonian. We show that the generalized time-dependent wave operator can be used to correct easily the adiabatic approximation which is very imperfect in this situation.

High resolution microstructure characterization of the interface between cold sprayed Al coating and Mg alloy substrate

High-resolution transmission electron microscopy (HR-TEM) has validated the intimate metallurgical (atomic) bond formed along the interface of a cold-sprayed Al coating upon an Mg-alloy (AZ91) substrate. The compressive impact led to the formation of nanostructured layers of about 300–500nm into the substrate. A highly distorted lattice structure with the inclusion of small amorphous zones was observed at the periphery of the particle/substrate interface, as a result of adiabatic shear plastic deformation at a high strain rate.

Effect of discharge voltage on the deformation of Ti Grade 1 rivet in electromagnetic riveting

Discharge voltage is one of the most important parameters in electromagnetic riveting. The effect of discharge voltage on the deformation of Ti Grade 1 rivet was investigated by experiment from macro and micro-scales in low voltage electromagnetic riveting. The result shows that the amplitude of the discharge current, the riveting force and the rivet deformation increases with the discharge voltage. The deformation in the rivet head is inhomogeneous and there are three deformation zones, viz., large, small and difficult deformation zones. The deformation in rivet shaft is quite uniform. The deformation of Ti Grade 1 rivet is an adiabatic process and the deformation mechanism is adiabatic shearing deformation. With the increase of discharge voltage, adiabatic shear band gets more and more obvious and the grains inside the adiabatic shear band are elongated severely and re-arranged along the direction of the adiabatic shear band. A model for the modeling of grain deformation inside the adiabatic shear band is proposed. When the adiabatic temperature does not affect the flow of the material, the process of microstructure evolution mechanism of Ti Grade 1 rivet in electromagnetic riveting is mainly the twinning deformation. With the increase of rivet deformation, it is the sub-grain rotation to complete the dynamic recrystallization. These findings provide an in-depth understanding of Ti Grade 1 rivet deformation mechanism and a basis for process determination and quality assurance of the electromagnetic riveting process.

Constrained quantum particles and geometric phases in noninertial frames

We consider particles constrained to move in the close vicinity of a space curve through a steep quadratic potential in the plane normal to the curve. As is known, the effective 1D Hamiltonian that governs the motion along the curve involves both its curvature and torsion. Thus, the adiabatic cyclic deformations of the curve might give rise to geometric phases being accumulated by the particle. We report that this is indeed, in general, the case, and analyze in detail the origin of the phases, as described in both an inertial Cartesian frame and a noninertial one, adapted to the curve. We extend previous work to include non-locally arclength preserving deformations, and derive general formulas for Berry’s curvature in this case.