Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum Cycle in Relativistic Non-Commutative Space with Generalized Uncertainty Principle correction
83
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as its working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structure is changed? In this paper, two different working substance in non-commutative spacetime with relativistic and generalized uncertainty principle corrections has been considered for the analysis of the efficiency of the heat engine cycles. The efficiency of the quantum heat engine gets a boost for higher values of the non-commutative parameter with a harmonic oscillator as the working substance. In the case of the second working medium (one-dimensional infinite potential well), the efficiency shows a constant result in the non-commutative space structure.
rate research
Read More
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrodinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two important principles. If a logical quantum system is encoded into $n$ physical subsystems, we say that the code is covariant with respect to a symmetry group $G$ if a $G$ transformation on the logical system can be realized by performing transformations on the individual subsystems. For a $G$-covariant code with $G$ a continuous group, we derive a lower bound on the error correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems $n$ or the dimension $d$ of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with $n$ or $d$ as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large $d$ (using random codes) or $n$ (using codes based on $W$-states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.
Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $beta_0<5 times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $beta_0 ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control.
We discuss classical electrodynamics and the Aharonov-Bohm effect in the presence of the minimal length. In the former we derive the classical equation of motion and the corresponding Lagrangian. In the latter we adopt the generalized uncertainty principle (GUP) and compute the scattering cross section up to the first-order of the GUP parameter $beta$. Even though the minimal length exists, the cross section is invariant under the simultaneous change $phi rightarrow -phi$, $alpha rightarrow -alpha$, where $phi$ and $alpha$ are azimuthal angle and magnetic flux parameter. However, unlike the usual Aharonv-Bohm scattering the cross section exhibits discontinuous behavior at every integer $alpha$. The symmetries, which the cross section has in the absence of GUP, are shown to be explicitly broken at the level of ${cal O} (beta)$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
