Bound Entanglement in Thermalized States and Black Hole Radiation
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Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high-energy to condensed-matter physics. Quantum computers may provide a way to solve this problem efficiently. Preparing a thermal state on a quantum computer is challenging, but there exist methods to circumvent this by computing a weighted sum of time-dependent matrix elements in a convenient basis. Further, while the number of basis states can be large, in this paper we show that it can be reduced by simulating only the largest density matrix elements by weight, capturing the density matrix to a specified precision. Leveraging Hamiltonian symmetries enables further reductions. This approach paves the way to more accurate thermal-state dynamics simulations on near-term quantum hardware.
Thermal maturity of source rocks indicated by vitrinite reflectance (R o ) is an important and reliable parameter to determine the petroleum potential of sedimentary basins. Originally, R o was used to characterize the degree of coalification of coals and thus works well for coal seams, but it has limitations when used to determine the thermal maturity of black shale successions. A suite of six coal-shale pairs from the Upper Devonian black shale formations in the eastern United States (New Albany Shale, Ohio Shale, Dunkirk Shale, and Rhinestreet Shale) was selected to study the applicability of R o in assessing the thermal maturity of black shale successions. The results show that vitrinite in the studied coal samples is dominated by collotelinite, whereas vitrinite in black shales occurs as small dispersed particles (~5 μm) in the mineral matrix. When comparing the size and morphology of dispersed vitrinite particles in shales and collotelinite fragments in coals, vitrinite in shales and adjacent coals should have the same origin. The measured mean random R o of vitrinite in coals ranges from 0.51–0.68%, and is 0.04–0.11% (average 0.07%) lower than that of dispersed vitrinite particles in enclosing shales. This observation contrasts with previously reported R o suppression in liptinite-rich black shales. A high standard deviation of R o measurements indicates a highly heterogeneous nature of vitrinite in black shales. Three mechanisms can be envisioned to contribute to the higher R o of dispersed vitrinite particles in black shales relative to enclosed coals. First, small vitrinite particles may become more oxidized because small particles are more frequently suspended during transport to the site of deposition and reworking of bottom sediments after deposition than large pieces of driftwood that will turn into enclosed coal lenses during burial diagenesis. Second, misidentification of zooclast (e.g., chitinozoan) fragments as vitrinite due to loss of diagnostic morphology. Third, various macerals in the vitrinite group (e.g., corpogelinite and collotelinite) may have had different original reflectance values. Based on the petrographic characteristics of vitrinite and vitrinite-like particles, caution should be applied when using the R o values of dispersed vitrinite and vitrinite-like particles in black shales as indicators of thermal maturity.
Thermal demand for heating and cooling has been predominantly supplied by fossil fuel combustion in the United States, although low-carbon alternatives are extensively available including geothermal, solar thermal, and waste heat. Here, this study analyzed end-use energy consumption, fuel expenditure, and data center commissioned power data to geospatially characterize the U.S. low-temperature heating and cooling demand at the county level in residential, commercial, manufacturing, agricultural, and data center sectors and understand potential opportunities for geothermal applications. In the analysis, the regional-scale energy consumption data was incorporated with system efficiencies to address actual demand and was then disaggregated with weighting factors to the county level. The results indicated that total low-temperature heating and cooling demand is 16.7 EJ, combining heating demand of 10.8 EJ and cooling demand of 5.9 EJ. Overall, 59.9 % (10 EJ) of the low-temperature heating and cooling demand occurred in the residential sector. The heating and cooling demand visualized in maps represented that the geospatial distribution of heating and cooling demand in the residential and commercial sectors is governed by the number of housing units and climate zone designations, while heating and cooling demand in the manufacturing, agricultural, and data center sectors is dependent on the number and location of facilities. The results also demonstrated that geothermal heat pumps are broadly used in the residential and commercial sectors for heating and cooling in the U.S. Midwest, South, and Northeast regions but are limited in the West, implying great decarbonization potential in the future.
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.
The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.
A thermally sensitive ionic redox transistor comprises a channel, a reservoir layer, and an electrolyte layer disposed between the channel and the reservoir layer. A conductance of the channel is varied by changing concentration of ions in the channel layer. The electrolyte layer is configured to undergo a state change at a state transition temperature. Below the state transition temperature, ions in the electrolyte layer are substantially immobile. Above the state transition temperature, ions can move freely between the reservoir layer and the channel across the electrolyte layer in response to a voltage being applied between the channel and the reservoir layer. When the device is cooled below the state transition temperature or temperature range, the ions are trapped in one or more of the layers because the electrolyte layer loses its ionic conductivity. A state of the redox transistor can be read by measuring the conductance of the channel.
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A whole-core, steady-state thermal-hydraulic model is developed for the fluoride-salt-cooled small modular advanced high-temperature reactor (SmAHTR) that employs an annular fuel configuration. This pre-conceptual reactor design by Oak Ridge National Laboratory (ORNL) has the annular fuel and moderator pins arranged in a hexagonal layout. The FLiBe coolant flows from the bottom to the top of the core, parallel to the hexagonal bundle. The fuel and moderator pins in the core are discretized into finite volumes and the 3-D heat conduction equation is solved to obtain the temperature profile. Inter-fuel assembly conduction is also addressed. For this fuel assembly configuration, the coolant flows through two distinct regions – the hexagonal pin bundle and the annulus between the fuel pin and the tie rod. The fluid flow through the hexagonal bundles is modeled using the subchannel approach, in which the coolant region is discretized into corner, edge and interior subchannels and the resulting conservation equations are systematically solved. The 1-D mass, momentum and energy equations are solved for the annulus channels between the fuel pin and the tie rod. Pertinent closure models from the literature are employed to close the system of equations. We also performed a preliminary code-to-code comparison between the present model and a CFD model.. The resulting thermal-hydraulic model can provide temperature, flow rate and pressure drop profiles for the different solid and fluid regions throughout the entire core. Whole-core thermal-hydraulic results for a representative power profile are presented and discussed.
This paper presents results of steady-state thermal-hydraulic analysis for the designed working core of the Dalat Nuclear Research Reactor (DNRR) using the PLTEMP/ANL code. The core was designed to be loaded with 92 low-enriched uranium (LEU) VVR-M2 fuel bundles (FBs) and 12 beryllium rods surrounding a neutron trap at the core center, for replacement of the previous core with 104 high-enriched uranium (HEU) VVR-M2 FBs. Before using this code for thermohydraulic analysis of the designed LEU working core, it was validated by comparing calculation results with experimental data collected from the HEU working core of the DNRR. The discrepancy between calculated results and measured data was at the maximum about 0.8°C and 1.5°C of fuel cladding and outlet coolant temperatures, respectively. In the design calculation, thermohydraulic safety was confirmed through evaluation of the fuel cladding and coolant temperatures, as well as of other safety parameters such as Departure from Nucleate Boiling Ratio (DNBR) and Onset of Nucleate Boiling Ratio (ONBR). The calculation results showed that, in normal operation conditions at full nominal thermal power of 500 kW without uncertainty parameters, the maximum fuel cladding temperature of the hottest FB was about 90.4°C, which is lower than its limit value of 103°C, the minimum DNBR was 32.0, which is much higher than the recommended value of 1.5, and the minimum ONBR was 1.43, which is higher than the recommended value of 1.4 for VVR-M2 LEU fuel type. When the global and local hot channel factors were taken into account, the maximum temperature of fuel cladding at the hottest FB was about 98.4 °C, for global only, and 114.3°C, for global together with local hot channel factors. The calculation results confirm the safety operation of the designed LEU core loaded with 92 fresh VVR-M2 FBs.
Understanding heat transfer in the earth mantle region is of great scientific interest but highly challenging due to dissimilar conditions from our daily lives. Thermal conductivity of highly pressured and thermally activated materials can be completely different from that at ambient condition. In this study we calculate the equation of state and thermal conductivity of cubic crystalline MgO, a major component of the mantle, in such an environment. It is shown that the material properties are not accurately captured unless rigorous treatment of anharmonicity of phonon vibrational motion is explicitly applied. To predict renormalized phonon dispersion relations, interatomic force constants of high-order expansion are required, especially at elevated temperature. The anharmonicity plays an increasingly substantial role for regulating volume expansion as temperature rises, because the Gibbs free energy of MgO considerably deviates from what was predicted by the quasiharmonic approximation. We find that the lattice thermal conductivity of MgO and the heat transfer of the earth's mantle are reliably estimated only when both the temperature-dependent renormalization of phonon frequencies and four-phonon scattering effects are taken into consideration. We map the characteristics at Geotherm into contour diagrams in which equilibrium volumes and the thermal conductivities are described as functions of temperature and pressure. Furthermore, the thermal conductivity values of MgO in this study are smaller than those in previous theoretical studies due to the additional incorporation of four-phonon scatterings in the calculations. Specifically, deviation between the values in previous studies and in this study becomes larger as thermodynamic variables reach those near the core-mantle boundary. For instance, thermal conductivities of 52.15 and 23.67 Wm -1 K -1 are estimated at ambient and extreme conditions (T = 4000K and P = 135 GPa), respectively.
With the expectation of near-immediate carbon neutrality, widespread implementation of proven High-Temperature Gas-cooled Reactors (HTGRs) embodies a viable solution pathway given their inherent, passive safety features and high thermal efficiency. This study provides an overview of the current state of research involving the thermal hydraulics associated with air ingress from a depressurized loss of forced cooling (D-LOFC) in HTGRs. Accurately characterizing and predicting the physical phenomena underlying air ingress is of paramount concern, as the integrity of the fuel and core graphite support structures are threatened by the presence of oxygen. Broadly speaking, the air ingress scenario can be delineated into three main stages: (1) Depressurization, (2) Density-Driven Flow, and (3) Natural Convection. In tandem with the underlying fundamental theory, this review collates and synthesizes the existing body of contemporary research concerning the air ingress scenario following a D-LOFC. As evinced by this review, our current understanding and predictive abilities have benefited from extensive research, predominantly concentrated on the rate of air ingestion into the core. Here, additional research is necessary to holistically capture the phenomenology of an air ingress scenario following a D-LOFC by considering an additional variable: the oxygen content of the ingressing air. The latter variable requires investigation into the complex interactions of the fully integrated system. Additionally, while numerical tools are evolving domestically through the Nuclear Energy Advanced Modeling and Simulation program, a sufficiently validated code remains absent.
Materials with tunable thermal properties enable on-demand control of temperature and heat flow, which is an integral component in the development of solid-state refrigeration, energy scavenging, and thermal circuits. Although gap-based and liquid-based thermal switches that work on the basis of mechanical movements have been an effective approach to control the flow of heat in the devices, their complex mechanisms impose considerable costs in latency, expense, and power consumption. As a consequence, materials that have multiple solid-state phases with distinct thermal properties are appealing for thermal management due to their simplicity, fast switching, and compactness. Thus, an ideal thermal switch should operate near or above room temperature, have a simple trigger mechanism, and offer a quick and large on/off switching ratio. In this study, we experimentally demonstrate that manipulating phonon scattering rates can switch the thermal conductivity of antiferroelectric PbZrO 3 bidirectionally by –10% and +25% upon applying electrical and thermal excitation, respectively. Our approach takes advantage of two separate phase transformations in PbZrO 3 that alter the phonon scattering rate in different manners. In this study, we demonstrate that PbZrO 3 can serve as a fast (<1 second), repeatable, simple trigger, and reliable thermal switch with a net switching ratio of nearly 38% from ~1.20 to ~1.65 W m –1 K –1 .
Active insulation systems (AISs) in buildings are envelopes that integrate thermal insulation, thermal energy storage, and controls. Although different designs for AISs have been proposed in the literature, a comprehensive analysis of feasible AISs is lacking. This paper discusses the energy performance, peak demand reduction potential, and performance characteristics of an AIS that uses a concrete wall as thermal mass sandwiched between two solid-state thermal switches (STSs). These STSs change their thermal conductivity using an on/off metal switch to create or break a thermal bridge across the STS. This paper first describes the experimental setup, used to determine the ratio of thermal resistance during R-high (low thermal conductivity) and R-low (high thermal conductivity) states of the STSs. This ratio was then used in whole-building energy simulations to evaluate the performance of AIS walls across different climate zones with/without a freeze timer of 60 min. The timer was added to reduce the number of switches of STSs from one state to another, and hence the energy needed for these switches. Analysis of the switching frequency and interval of STSs, thermal conductivity of walls, impact of wall orientation, and heat transfer through the wall from the use of AIS at different climate zones/locations were performed. The simulation results show that the AIS can achieve energy savings ranging from ~980 to 2,290 kWh in a single-family home with a floor area of ~220 m 2 compared with an IECC 2018 baseline. We found the energy savings was higher in dry climate zones which represent 17% of residential buildings in the United States, compared to humid or marine climate.
We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024
A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N f =0) and “real-world” (N f =2+1 at physical quark masses) QCD. In this IR phase, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra (λ IR = 0, ±λ A ≠ 0), as manifested in the dimension function d IR (λ). Here, we present the first evidence, based on lattice QCD calculation at a=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at T = 234 MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity (d IR = 3 to d IR ≃ 2), similar to the IR phase of pure-glue QCD, at T = 187 MeV we observe a continuous λ-dependence. This suggests that thermal states just above the chiral crossover are non-analytically (in T) connected to thermal state at T = 234 MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.
Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To illustrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.