Phases For Mixed States Research Articles

Mixed-State Quantum Phases: Renormalization and Quantum Error Correction

Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their two-way connectivity via local quantum channels, we use the renormalization group (RG) and decoders of quantum error correcting codes. We introduce a real-space RG scheme for mixed states based on local channels which ideally preserve correlations with the complementary system, and we prove this is equivalent to the reversibility of the channel’s action. As an application, we demonstrate an exact RG flow of finite temperature toric code in two dimensions to infinite temperature, thus proving it is in the trivial phase. In contrast, for toric code subject to local dephasing, we establish a mixed-state toric code phase using local channels obtained by truncating an RG-type decoder and the minimum weight perfect matching decoder. We also discover a precise relation between mixed-state phase and decodability, by proving that local noise acting on toric code cannot destroy logical information without bringing the state out of the toric code phase. Published by the American Physical Society 2024

Symmetry-Enforced Many-Body Separability Transitions

We study quantum many-body mixed states with a symmetry from the perspective of , i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decohered p+ip superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition. Published by the American Physical Society 2024

Effect of mixed carbon phase state on detonation parameters and reaction zone of explosives under extreme condition

A precise description of the thermodynamic states of gaseous and solid detonation products is essential when using thermodynamic calculations to determine the detonation performance and destructive power of explosives. For high oxygen-lean explosives (the oxygen contained in explosives is insufficient to completely oxidize combustible elements and excess solid carbon will be generated in the detonation products), the phase state of solid carbon product affects the Chapman–Jouguet (CJ) detonation performance parameters, reaction zone, and energy release process. However, the recovery of detonation products demonstrates that the actual detonation carbon product is primarily a mixed state of diamond/graphite stack, as opposed to the existing thermodynamic codes, which essentially treat detonation carbon as single-phase carbon. To understand the thermodynamic effect of the mixed carbon phase state on the non-ideal detonation behavior, in this work, the matching relationship among the VINET equation of state parameters, thermodynamic potential parameters of the solid products of the equivalent system and the phase mixed system was constructed by using the nonlinear fitting method. The relationship between the carbon phase composition at the CJ point and the explosive composition structure was researched. Investigations were conducted into how the mixed carbon phase affected the volume and content of gas products as well as the composition at CJ points. Diamond formation in products is good for enhancing explosive's working capacity. Based on mixed-state potential parameters, the correlation mechanism between the mixed carbon phase and the chemical reaction zone was investigated, and it was found that intramolecular carbon/intermolecular carbon and more detonation graphite/diamond products all would lead to the extension of the reaction zone.

From raw elements to 3D samples: An economical route for Co-Cr-Mo alloy fabrication

This study explores an efficient and feasible method for production of non-commercial Co-Cr-Mo powder feedstock for Laser Powder Bed Fusion (LPBF), employing mechanical alloying (MA) with following thermal treatment. Elemental Co, Cr, and Mo powders were subjected to MA to create a powder nanostructured composite. Initially, the mechanically alloyed powder had a mixed-phase state, with ε-phase as the main one (about 95 wt%) and impurities of Cr2O3. However, an additional 1.5-hour of isothermal annealing at 400 °C successfully reduced the Cr2O3 impurities and caused oxygen content to decrease, indicating a reduction in residual oxygen in the powder. This annealing process activated diffusion and induced relaxation of residual stresses, evidenced by decreased lattice microstrains: 0.8% for the Co-phase, 0.2% for both the Cr-phase and Mo-phase. Powder subjected to the thermal treatment was then utilized in LPBF to create bulk Co-Cr-Mo samples. The formed samples showed a typical LPBF microstructure represented by uniaxial cells and dendrites, with the distance between these structures not exceeding 3 µm. The samples showed homogenous elemental distribution, mixed-phase composition, and oxygen concentration not exceeding 5 wt%. In terms of mechanical properties, the LPBF samples exhibited a microhardness value of 4300 ± 200 MPa, ductility of 0.85, and yield strength of 1.4·103 MPa. Our method yields results comparable to those obtained from commercially spherical powder, indicating that our cost-effective approach does not sacrifice product quality. It represents a substantial cost reduction, approximately 4.5 times lower than that of commercial spherical powder, thereby highlighting the economic efficiency of our powder feedstock preparation for LPBF. Our findings underscore the potential of mechanically alloyed and thermally treated powder in LPBF. This worthwhile and efficient method of preparation powder feedstock breaks ground for more comprehensive facilities in 3D printing, cut down on cost of production with maintaining the high-quality output.

Revival of rhombohedral structure and complex magnetic response in (La,Cr) codoped BiFeO3

The polycrystalline ceramics of Bi0.83La0.17Fe1-xCrxO3 (BLFCO) have been synthesized by the solid-state reaction method to investigate the features of structural phase coexistence and complex magnetic response. The coexistence of the R3c rhombohedral and Pbam orthorhombic structures has been revealed by X-ray diffraction and Rietveld refinement. Selected-area Raman scattering spectra are used to further confirm a mixed phase state as both phonon vibrations of these phases are detectable. An unusual revival of the R3c phase is observed with increasing chromium concentration. The compound displays an intriguing weak magnetic response and some unique phenomena, such as the magnetic aging and field step-dependent hysteresis loop. The electric-field-controlled magnetism shows a complex behavior due to the interplay of the phase boundary ferromagnetism and structural phase transition.

Mixed phase ZnSnN2 thin films for solar energy applications: Insight into optical and electrical properties

Zinc tin nitride (ZnSnN2, ZTN) films synthesized by magnetron co-sputtering at a temperature close to the ZTN decomposition point and with the cation ratio close to stoichiometric have been studied to gain insight into their structural, optical and electrical properties. According to X-ray diffraction and Raman spectroscopy, the samples are polycrystalline with some disorder in the cation sublattice. Hall effect measurements reveal n-type conductivity and very high carrier density above 1019 cm−3. At the lowest carrier density, the mobility achieves the best value ∼19 cm2/(V*s), which is acceptable for device applications. The optical band gap shows a blue shift with increasing electron density, which is related to the increase in tin content and the Burstein-Moss effect. Analysis of the blue shift in terms of the Burstein-Moss effect theory gives a value of 1.43 eV for the intrinsic band gap of ZTN in the mixed-phase state.

Crystal and magnetic structures of solid solutions based on BiFeO3

The correlation between the multiphase state of the system and its magnetic properties was studied on Bi1–xEuxFeO3 ceramic samples in the range 0.12 ≤ x ≤ 0.18. The X-ray diffraction results indicate that, with an increase in the concentration of Eu ions, a structural transition from the rhombohedral (R3c) to nonpolar orthorhombic (Pnma) phase is observed through the partial formation of an antipolar orthorhombic structure (Pbam). The mixed phase state in the obtained compounds is observed in the range 0.12 ≤ x ≤ 0.16. Magnetic measurements in a strong magnetic field indicate a weak ferromagnetic interaction. The magnetic response in a strong field is explained by the location of the spins at the phase boundary, as well as by the presence of intrinsic antiferromagnetic spins.

Decline Mechanism of Graphite/Lithium Metal Hybrid Anode and Its Stabilization by Inorganic-Rich Solid Electrolyte Interface.

The graphite/lithium metal hybrid anode shows great potential for achieving high-specific-energy lithium batteries. Despite the "dead lithium" problem caused by repeated stripping and deposition of Li component based on a conversion reaction, the degradation mechanism, based on intercalation reaction, of graphite in a hybrid anode is generally ignored. In this contribution, through in situ X-ray diffraction and in situ Raman analysis, we reveal that hysteresis and the mixed-phase state of graphite during deintercalation play a critical role in hybrid battery degradation. On the other hand, we successfully mitigated graphite degradation and increased the reversible capacity of the hybrid anode by introducing an inorganic-rich solid electrolyte interface. Remarkably, the hybrid anode (30% higher specific capacity compared to graphite) exhibits an average coulombic efficiency of 99.11% and retains 96.13% of initial capacity over 120 cycles. This work sheds new light on the advancement of high-specific-energy lithium secondary batteries.

Imaging Field-Driven Melting of a Molecular Solid at the Atomic Scale.

Solid-liquid phase transitions are basic physical processes, but atomically-resolved microscopy has yet to capture their full dynamics. We have developed a new technique for controlling the melting and freezing of self-assembled molecular structures on a graphene field-effect transistor (FET) that allows phase transition behavior to be imaged using atomically-resolved scanning tunneling microscopy. This is achieved by applying electric fields to F4 TCNQ-decorated FETs to induce reversible transitions between molecular solid and liquid phases at the FET surface. Nonequilibrium melting dynamics are visualized by rapidly heating the graphene substrate with electrical current and imaging the resulting evolution toward new 2D equilibrium states. An analytical model has been developed that explains observed mixed-state phases based on spectroscopic measurement of solid and liquid molecular energy levels. The observed non-equilibrium melting dynamics are consistent with Monte Carlo simulations. This article is protected by copyright. All rights reserved.

Mixed state behavior of Hermitian and non-Hermitian topological models with extended couplings

Geometric phase is an important tool to define the topology of the Hermitian and non-Hermitian systems. Besides, the range of coupling plays an important role in realizing higher topological indices and transition among them. With a motivation to understand the geometric phases for mixed states, we discuss finite temperature analysis of Hermitian and non-Hermitian topological models with extended range of couplings. To understand the geometric phases for the mixed states, we use Uhlmann phase and discuss the merit-limitation with respect extended range couplings. We extend the finite temperature analysis to non-Hermitian models and define topological invariant for different ranges of coupling. We include the non-Hermitian skin effect, and provide the derivation of topological invariant in the generalized Brillouin zone and their mixed state behavior also. We also adopt mixed geometric phases through interferometric approach, and discuss the geometric phases of extended-range (Hermitian and non-Hermitian) models at finite temperature.

Size-Induced Ferroelectricity in Antiferroelectric Oxide Membranes.

Despite extensive studies on size effects in ferroelectrics, how structures and properties evolve in antiferroelectrics with reduced dimensions still remains elusive. Given the enormous potential of utilizing antiferroelectrics for high-energy-density storage applications, understanding their size effects will provide key information for optimizing device performances at small scales. Here, the fundamental intrinsic size dependence of antiferroelectricity in lead-free NaNbO3 membranes is investigated. Via a wide range of experimental and theoretical approaches, an intriguing antiferroelectric-to-ferroelectric transition upon reducing membrane thickness is probed. This size effect leads to a ferroelectric single-phase below 40nm, as well as a mixed-phase state with ferroelectric and antiferroelectric orders coexisting above this critical thickness. Furthermore, it is shown that the antiferroelectric and ferroelectric orders are electrically switchable. First-principle calculations further reveal that the observed transition is driven by the structural distortion arising from the membrane surface. This work provides direct experimental evidence for intrinsic size-driven scaling in antiferroelectrics and demonstrates enormous potential of utilizing size effects to drive emergent properties in environmentally benign lead-free oxides with the membrane platform.

Сorrelation between structural phase coexistence and magnetic response of Eu-doped BiFeO3 at the morphotropic phase boundary

Bi1-xEuxFeO3 ceramic samples with x = 0.1–0.2 have been synthesized to investigate the correlation between the multiphase coexistence and magnetic response. X-ray diffraction and Raman scattering spectra reveal the structural transition from the R3c rhombohedral to Pnma nonpolar orthorhombic structures via partial formation of Pbam antipolar orthorhombic structure with increasing of Eu concentration, thus disclosing the mixed phase state in the composition range of 0.10 ≤ x ≤ 0.18. The magnetic measurement at a high magnetic field reveals a weak ferromagnetic behavior; the magnetization reaches maximum value in phase mixture compounds and then decreases in a single phase compound. The different magnetic response under high and low applied fields is explained in terms of the phase boundary (PB) spins and the intrinsic antiferromagnetic spins. The characteristic of the PB spins contributing to the magnetic properties have been determined by the study on the magnetic aging effect, electric field-induced phase transition, and field step-dependent hysteresis loops.

Interplay of multiple structural phase and magnetic response of Bi1-xPrxFeO3 ceramics

The detailed structural phase transition induced by chemical substitution in Bi1-xPrxFeO3 (x = 0.1–0.2) polycrystalline ceramics is reported herein. Pr3+ substitution is observed to destabilize the polar R3c symmetry due to the chemical strain effect caused by the large ionic radius mismatch at the Bi-site. The R3c rhombohedral phase can only be stabilized up to 14 mol% of Pr doping (x < 0.14); the phase transition starts to appear at a higher Pr concentration (x ≥ 0.14), forming a morphotropic phase boundary between the R3c rhombohedral and Pbam orthorhombic phases. Increasing Pr concentration causes the magnetic transition from a pure antiferromagnetic to a weak ferromagnetic state as a result of the evolution of crystal structure. The influence of PB spins on the magnetic properties of Bi1-xPrxFeO3 compounds has been uncovered through manipulation of the mixed phase state by an electric field, temperature, and structural relaxation.

Membrane tension controls the phase equilibrium in fusogenic liposomes.

Fusogenic liposomes have been widely used for molecule delivery to cell membranes and cell interior. However, their physicochemical state is still little understood. We tested mechanical material behavior by micropipette aspiration of giant vesicles from fusogenic lipid mixtures and found that the membranes of these vesicles are fluid and under high mechanical tension even before aspiration. Based on this result, we developed a theoretical framework to determine the area expansion modulus and membrane tension of such pre-tensed vesicles from aspiration experiments. Surprisingly high membrane tension of 2.1 mN m−1 and very low area expansion modulus of 63 mN m−1 were found. We interpret these peculiar material properties as the result of a mechanically driven phase transition between the usual lamellar phase and an, as of now, not finally determined three dimensional phase of the lipid mixture. The free enthalpy of transition between these phases is very low, i.e. on the order of the thermal energy.

Erratum: Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states [Phys. Rev. B 101 , 104310 (2020)

Erratum: Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states [Phys. Rev. B <b>101</b> , 104310 (2020)

Ubiquity of zeros of the Loschmidt amplitude for mixed states in different physical processes and its implication

The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not associated with a phase transition. We present examples of two-level and three-level systems exhibiting finite- or infinite- temperature DQPTs and finite-temperature TQPTs associated with the Loschmidt-amplitude zeros. Moreover, the dynamical phase or geometrical phase of mixed states can be extracted from the Loschmidt amplitude. Those phases may become quantized or exhibit discontinuity at the Loschmidt-amplitude zeros. A spinor representation of the purified states of a general two-level system is presented to offer more insights into the change of purification in different processes. The quasistatic process, for example, is shown to cause a rotation of the spinor.

Phase-controlled field-effect micromixing using AC electroosmosis

The exploration and application of electrokinetic techniques in micro total analysis systems have become ubiquitous in recent years, and scientists are expanding the use of such techniques in areas where comparable active or passive methods are not as successful. In this work, for the first time, we utilize the concept of AC electroosmosis to design a phase-controlled field-effect micromixer that benefits from a three-finger sinusoidally shaped electrodes. Analogous to field-effect transistor devices, the principle of operation for the proposed micromixer is governed by the source-gate and source-drain voltage potentials that are modulated by introducing a phase lag between the driving electrodes. At an optimized flow rate and biasing scheme, we demonstrate that the source, gate, and drain voltage phase relations can be configured such that the micromixer switches from an unmixed state (phase shift of 0°) to a mixed state (phase shift of 180°). High mixing efficiencies beyond 90% was achieved at a volumetric flow rate of 4 µL/min corresponding to ~13.9 mm/s at optimized voltage excitation conditions. Finally, we employed the proposed micromixer for the synthesis of nanoscale lipid-based drug delivery vesicles through the process of electrohydrodynamic-mediated nanoprecipitation. The phase-controlled electrohydrodynamic mixing utilized for the nanoprecipitation technique proved that nanoparticles of improved monodispersity and concentration can be produced when mixing efficiency is enhanced by tuning the phase shifts between electrodes.

Chaotic photon spheres in non-Euclidean billiard

Abstract With the advancement in understanding of the physics inside chaotic systems, chaos has been harnessed from a nuisance to a beneficial factor in optical devices. Light–matter interaction in chaotic systems has been utilised for improving broadband energy harvesting and momentum transformations, achieving light localization beyond diffraction limit and even stabilizing the dynamics of high power laser. While extensive study about wave chaos has been made in deformed microcavities, investigation of how chaos dynamics evolves in curved space manifold remains elusive. Here, we study the non-Euclidean billiard of a torus-like manifold, which is a closed 2D cavity system with effective periodic boundaries. The ray chaotic behaviours on the deformed toroidal surface are explored using the geodesic equation. By tuning the deformation parameter of the torus, we observe the transition of the billiard from the ordered phase state to mixed phase states and then complete ray chaos. The photon sphere of the torus is identified as the transition position from ordered states to chaotic states. Compared with other chaotic behaviours resulted from the random scattering inside deformed cavities, we demonstrate chaotic dynamics purely on a curved surface, which may shed light on the better understanding of chaos in optics.

Visualization of compensating currents in type-II/1 superconductor via high field cooling

The morphology of vortex lattice domains in bulk type-II/1 superconductors is of central interest for many areas such as fundamental condensed matter physics, engineering science, and the optimization of materials for high transport current superconductivity applications. Here, we present a comprehensive experimental study of a single crystal niobium in the intermediate mixed state and Shubnikov phase with two complementary neutron techniques: high resolution polarized neutron imaging and small-angle neutron scattering. In this way, we were able to identify and visualize the occurrence of compensating currents, the flux line closure, and the freezing of the vortex spacing during the process of field cooling and high field cooling. With the combination of complementary neutron techniques, it was possible to add insights into the quest for the understanding of the flux pinning and nucleation of vortices in type-II/1 superconductors during the process of field cooling and high field cooling.

Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states

While a pure quantum state may accumulate both the Berry phase and dynamic phase as it undergoes a cyclic path in the parameter space, the situation is more complicated when mixed quantum states are considered. From the Ulhmann bundle, a mixed quantum state can accumulate the Ulhmann phase if the parallel-transport condition is satisfied. However, we show that the Ulhmann process is in general not compatible with the evolution equation of the density matrix governed by the Hamiltonian. Thus, a mixed quantum state usually accumulates a dynamic phase during its time evolution. We present the expression of the dynamic phase for mixed quantum states. In examples of quasi-static one-dimensional two-band models and simple harmonic oscillator, the dynamic phase can take multiple discrete values at infinitely high temperature due to the resonant points. However, the behavior differs if the energy spectrum is continuous without a band gap. Moreover, there is no natural analog of the dynamic phase in classical systems.