Hojman symmetry in f ( T ) $f(T)$ theory

Abstract

Today, f (T ) theory has been one of the popular modified gravity theories to explain the accelerated expansion of the universe without invoking dark energy. In this work, we consider the so-called Hojman symmetry in f (T ) theory. Unlike Noether conservation theorem, the symmetry vectors and the corresponding conserved quantities in Hojman conservation theorem can be obtained by using directly the equations of motion, rather than Lagrangian or Hamiltonian. We find that Hojman symmetry can exist in f (T ) theory, and the corresponding exact cosmological solutions are obtained. We find that the functional form of f (T ) is restricted to be the power-law or hypergeometric type, while the universe experiences a power-law or hyperbolic expansion. These results are different from the ones obtained by using Noether symmetry in f (T ) theory. Therefore, it is reasonable to find exact cosmological solutions via Hojman symmetry.

Thermoelectric properties of nanocrystalline Cu3SbSe4 thin films deposited by a self-organized arrested precipitation technique

“…This value is comparable with our previously reported 5 microwave assisted Cu 3 SbSe 4 (0.14 at 300 K) [31] and also with CuSb 0.98 Ti 0.02 Se 2 (0.0041 at 300 K) [18]. But lower than reported in Cu 3 Sb 0.98 Bi 0.02 Se 4 (0.7 at 600 K) [12], in Cu 3 Sb 0.975 Sn 0.025 Se 4 (0.75 at 673 K) [20], in Cu 3 Sb 0.94 Sn 0.06 Se 3.5 S 0.5 (1.1 at 700 K) [24], in Cu 3 Sb 0.98 Sn 0.02 Se 4 (1.05 at 700 K) [25], in Cu 3 SbSe 4 10 (0.30 at 550 K) [28], in Cu 2.925 SbSe 4 (0.50 at 673 K) [29], in Cu 2.95 Sb 0.98 Sn 0.02 Se 4 (~0.7 at 673 K) [30] and in Cu 3 Sb 0.97 Al 0.03 Se 4 (0.58 at 600 K) [44]. This reported value might be improved at higher temperatures or may be with controlled addition of different dopant.…”

“…et al 65 [24][25] have reported low-temperature co-precipitation route and by doping of metal this group have achieved highest ZT value 1.1 at 700 K. Low temperature solvothermal method was also reported to synthesize plank-like crystals [26] and recently nanocrystals of Cu 3 SbSe 4 have been reported by hot-injection 70 method having bang gap 1.31 eV [14]. Last year Tyagi et al [27][28] and Wei et al [29][30] have reported mechanical fusion, followed by spark plasma sintering method for synthesis of this material. Also last year we have reported microwave assisted synthesis technique for deposition of Cu 3 SbSe 4 thin films [31].…”

Thermoelectric properties of Sn-doped p-type Cu3SbSe4: a compound with large effective mass and small band gap

“…A Cu deciency is chosen to compensate for Se volatilization and achieve the best performance, which was discussed in detail in a previous report. 25 A mixture of Cu, Sb, Sn and Se powders of high purity were milled in a stainless steel vessel on a planetary ball mill at 425 rpm for 10 hours protected by a mixed atmosphere of 95 vol% Ar and 5 vol% H 2 gases and were then milled in an alcohol solution. The as-synthesized powders were sintered by SPS at 703 K for 5 min under a uniaxial pressure of 50 MPa into disk-shaped samples about 3 mm in thickness and about 93% or higher in relative density.…”

Thermoelectric Properties of Indium(III)‐Doped Copper Antimony Selenide Thin Films Deposited Using a Microwave‐Assisted Technique

“…Cu‐Sb‐Se is a very efficient and capable optoelectronic material . It has been prepared by several methods such as direct fusion, solid‐state reaction, electrodeposition, spark plasma method, solvothermal method, co‐precipitation, rapid injection, hot injection and microwave‐assisted method . The microwave‐assisted technique is a promising method for the synthesis of nanocrystalline metal chalcogenide thin films.…”