Exact calculations of the thermal properties of two-electron GaAs quantum dots with inverse-square interactions

2021 ◽  
pp. 1-8
Author(s):  
F.S. Nammas ◽  
Eyad Hasan Hasan ◽  
A.N. Alnowafa
Keyword(s):  
Quantum Dots ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Low Temperature ◽  
Three Dimensional ◽  
Interaction Strength ◽  
Temperature Limit ◽  
Oscillator System ◽  
High Temperature Limit ◽  
Impressive Result

In this study, we theoretically scrutinize the effect of the inverse-square interaction on the thermal properties of two electrons trapped in a parabolic GaAs quantum dot. The analytical energy spectrum was used to calculate the thermal properties of the system using the canonical ensemble formalism. It was found that the thermal energy increased with the increase in temperature, while it remained almost constant for sufficiently low temperatures; it was also demonstrated that the inverse-square interaction increased the thermal mean energy. Moreover, the heat capacity increased sharply within a low-temperature window and saturated to the value of 2kB in the high-temperature limit. As expected, entropy increased linearly with increasing temperature. It was also shown that both entropy and heat capacity decreased rapidly when the confinement strength increased (or the dot size decreased) in the low-temperature limit, regardless of the influence of the interaction between the electrons. We also show that the number of allowed states of the system decreased as the interaction strength increased (Z(λ = 0) > Z(λ ≠ 0)). Finally, the stability of the system was investigated through F–T curves. The three-dimensional surface for the temperature-dependent mean energy and heat capacity was also plotted. It should be noted that, for the thermal mean energy, partition function, and Helmholtz free energy, the normal physical behavior of the two-oscillator system with Fermi statistics is recovered for λ → 0. However, heat capacity and entropy show exact two-fermion oscillator system behavior. The most impressive result found in this work is that the inverse-square interaction does not affect the heat capacity and entropy at all despite its noticeable effects on the thermal mean energy. This, in turn, facilitates theoretical studies related to finding the distinctive parameters of quantum dots without going into the heavy calculations resulting from the effects of interactions.

scholarly journals GENERALIZED PARTITION FUNCTIONS AND INTERPOLATING STATISTICS

1998 ◽  
Vol 13 (11) ◽  
pp. 843-852 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Limit ◽  
Partition Functions ◽  
High Temperature Limit ◽  
Full Temperature ◽  
Generalized Partition ◽  
Relativistic Particles

We show that the assumption of quasiperiodic boundary conditions (those that interpolate continuously periodic and antiperiodic conditions) in order to compute partition functions of relativistic particles in 2+1 space–time can be related with anyonic physics. In particular, in the low temperature limit, our result leads to the well-known second virial coefficient for anyons. Besides, we also obtain the high temperature limit as well as the full temperature dependence of this coefficient.

scholarly journals Effects of Vacancy Cluster Defects on Electrical and Thermodynamic Properties of Silicon Crystals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Pei-Hsing Huang ◽  
Chi-Ming Lu
Keyword(s):  
Heat Capacity ◽  
Debye Temperature ◽  
Density Functional ◽  
Phonon Dispersion ◽  
Vacancy Cluster ◽  
Temperature Limit ◽  
Phase Changes ◽  
Hexagonal Ring ◽  
High Temperature Limit ◽  
Silicon Crystals

A first-principle plane-wave pseudopotential method based on the density function theory (DFT) was employed to investigate the effects of vacancy cluster (VC) defects on the band structure and thermoelectric properties of silicon (Si) crystals. Simulation results showed that various VC defects changed the energy band and localized electron density distribution of Si crystals and caused the band gap to decrease with increasing VC size. The results can be ascribed to the formation of a defect level produced by the dangling bonds, floating bonds, or high-strain atoms surrounding the VC defects. The appearance of imaginary frequencies in the phonon spectrum of defective Si crystals indicates that the defect-region structure is dynamically unstable and demonstrates phase changes. The phonon dispersion relation and phonon density of state were also investigated using density functional perturbation theory. The obtained Debye temperatureθDfor a perfect Si crystal had a minimum value of 448 K atT= 42 K and a maximum value of 671 K at the high-temperature limit, which is consistent with the experimental results reported by Flubacher. Moreover, the Debye temperature decreased with increases in the VC size. VC defects had minimal effects on the heat capacity (Cv) value when temperatures were below 150 K. As the temperature was higher than 150 K, the heat capacity gradually increased with increasing temperature until it achieved a constant value of 11.8 cal/cell·K. The heat capacity significantly decreased as the VC size increased. For a 2 × 2 × 2 superlattice Si crystal containing a hexagonal ring VC (HRVC10), the heat capacity decreased by approximately 17%.

Temperature Dependence Electron-Impurity Scattering Rate in Doped Bilayer Graphene

2013 ◽  
Vol 665 ◽  
pp. 154-158
Author(s):  
Digish K. Patel ◽  
K.N. Vyas ◽  
A.C. Sharma
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Single Layer ◽  
Impurity Scattering ◽  
Temperature Limit ◽  
Bilayer Graphene ◽  
Particle Energy ◽  
Experimental Result ◽  
High Temperature Limit ◽  
Scattering Rate

Apart from its promising new material for technological innovations and applications, graphene offers a new and novel physics. In recent past, both single layer and bilayer Graphene have extensively been studied. Properties of Graphene sharply differ from that of 2DEG observed in doped semiconductor heterostructures. One of the important properties requisite for device making is charge transport. It has been suggested that considering a scattering mechanism based on screened charged impurities, one can obtain from a Boltzmann equation approach a conductivity that agrees with the experimental result on graphene. In this paper, we present a calculation of electron-impurity scattering rate, as a function of quasi particle energy ε measured from Fermi energy εf, in doped bilayer graphene for both high temperature TTf and low temperature TTf regimes. In the low temperature limit, we observe dip at normalized energy y=1.0, which is absent in the high temperature limit. Our numerical calculation shows that scattering rate remains almost constant with temperature in both regimes.

scholarly journals Experimental investigation of the ecological hybrid refrigeration cycle

2014 ◽  
Vol 35 (3) ◽  
pp. 145-154
Author(s):  
Piotr Cyklis ◽  
Ryszard Kantor ◽  
Tomasz Ryncarz ◽  
Bogusław Górski ◽  
Roman Duda
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Heat Source ◽  
Waste Heat ◽  
Temperature Limit ◽  
Working Fluid ◽  
Temperature Cycle ◽  
Compression System ◽  
High Temperature Limit ◽  
University Of Technology

Abstract The requirements for environmentally friendly refrigerants promote application of CO2 and water as working fluids. However there are two problems related to that, namely high temperature limit for CO2 in condenser due to the low critical temperature, and low temperature limit for water being the result of high triple point temperature. This can be avoided by application of the hybrid adsorption-compression system, where water is the working fluid in the adsorption high temperature cycle used to cool down the CO2 compression cycle condenser. The adsorption process is powered with a low temperature renewable heat source as solar collectors or other waste heat source. The refrigeration system integrating adsorption and compression system has been designed and constructed in the Laboratory of Thermodynamics and Thermal Machine Measurements of Cracow University of Technology. The heat source for adsorption system consists of 16 tube tulbular collectors. The CO2 compression low temperature cycle is based on two parallel compressors with frequency inverter. Energy efficiency and TEWI of this hybrid system is quite promising in comparison with the compression only systems.

DIMENSIONAL TRANSITIONS OF DENSITY OF STATES AND HEAT CAPACITY IN SPHERICAL QUANTUM DOTS

2008 ◽  
Vol 22 (15) ◽  
pp. 2373-2382
Author(s):  
SEUNG JOO LEE ◽  
HEE CHANG JEON ◽  
TAE WON KANG ◽  
SATOFUMI SOUMA
Keyword(s):  
Quantum Dots ◽  
Heat Capacity ◽  
Density Of States ◽  
Three Dimensional ◽  
Potential Barrier Height ◽  
Low Density ◽  
Barrier Thickness ◽  
Spherical Quantum Dot ◽  
Thin Barrier ◽  
Density Regime

We evaluate analytically and numerically the density of states (DOS) and the heat capacity in a spherical quantum dot formed by a spherical thin barrier. The control of the spherical barrier thickness or the potential barrier height is found to cause the dimensional transition from the three-dimensional (3D) behavior to the quasi-zero dimensional (Q0D) behavior in the DOS and the heat capacity. When the barrier is thick enough, the DOS shows the Q0D-like behavior but when the barrier is thin enough to allow electrons to tunnel through it, the temperature dependence of the heat capacity exhibits quite a distinct behavior depending on the electron density. Explicit numerical plots are given in the low density regime.

Crystal lattice disorder and characteristic features of the low-temperature thermal properties of higher borides

2020 ◽  
Vol 49 (7) ◽  
pp. 2138-2144 ◽  
Author(s):  
V. V. Novikov ◽  
A. V. Matovnikov ◽  
N. V. Mitroshenkov ◽  
A. V. Shevelkov ◽  
S. L. Bud'ko
Keyword(s):  
Heat Capacity ◽  
Thermal Properties ◽  
Low Temperature ◽  
Crystal Lattice ◽  
Lattice Parameters ◽  
Lattice Disorder ◽  
Characteristic Features

Heat capacity CP(T) and lattice parameters a(T), b(T) and c(T) of LuB44Si3.5 borosilicide are experimentally studied as a function of temperature in the range of 2–300 K.

Facile low-temperature synthesis of hematite quantum dots anchored on a three-dimensional ultra-porous graphene-like framework as advanced anode materials for asymmetric supercapacitors

2016 ◽  
Vol 4 (29) ◽  
pp. 11247-11255 ◽  
Author(s):  
Yunyong Li ◽  
Haiyan Zhang ◽  
Shanxing Wang ◽  
Yingxin Lin ◽  
Yiming Chen ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Low Temperature ◽  
Electrochemical Performance ◽  
Anode Materials ◽  
Three Dimensional ◽  
Asymmetric Supercapacitors ◽  
Low Temperature Synthesis ◽  
Temperature Synthesis ◽  
Porous Graphene

Hematite quantum dots anchored on a 3D ultraporous graphene-like framework as anode materials showed superior electrochemical performance for asymmetric supercapacitors.

Exact Solution of Heat Conduction in a Two-Domain Parallelepiped With an Orthotropic Layer and Its Application to the Estimation of the Three-Dimensional Thermal Conductivity Tensor and Volumetric Heat Capacity of the Orthotropic Layer

2002 ◽  
Author(s):  
Cuauhtemoc Aviles-Ramos
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Exact Solution ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Hybrid Algorithm ◽  
Three Dimensional ◽  
Volumetric Heat Capacity ◽  
Parameter Estimation Problem ◽  
Orthotropic Layer

The three-dimensional exact solution of heat conduction in a two-layer composite is found applying the method of separation of variables. One layer is orthotropic and the other layer is isotropic. This solution is used to calculate sensitivity coefficients with respect to the thermophysical properties of the orthotropic layer at fourteen thermocouple locations. Numerical experiments are carried out to solve a parameter estimation problem that involves the estimation of the thermal conductivities in the x-, y-, and z-directions, the volumetric heat capacity of the orthotropic layer, the effective thermal conductivity of the isotropic layer, and the heat flux input. The exact solution is used to generate temperature readings at fourteen thermocouple locations. First, the parameter estimation problem is solved using the exact temperatures and a hybrid algorithm to estimate the thermal properties and the heat flux. Second, random noise is added to the exact temperatures and the thermal properties and heat flux are estimated using the same hybrid algorithm. It is found that when using the exact temperatures, the minimized quadratic functional has a value of 2.4×10−16 (°C)2 and the estimated properties agree to the ninth decimal place with the “exact” properties.

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