| 1. |
- Aydin, Alhun, et al.
(author)
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Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases
- 2015
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In: Physica Scripta. - 0031-8949 .- 1402-4896. ; 90
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Journal article (peer-reviewed)abstract
- An ideal Maxwell–Boltzmann gas confined in various rectangular nanodomains is considered underquantum size effects. Thermodynamic quantities are calculated from their relations with the partitionfunction, which consists of triple infinite summations over momentum states in each direction. Toobtain analytical expressions, summations are converted to integrals for macrosystems by acontinuum approximation, which fails at the nanoscale. To avoid both the numerical calculation ofsummations and the failure of their integral approximations at the nanoscale, a method which gives ananalytical expression for a single particle partition function (SPPF) is proposed. It is shown that adimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore,to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather thannumerical calculation of summations. Considering rectangular domains with different aspect ratios, acomparison of the results of derived expressions with those of summation forms of the SPPF is made.It is shown that analytical expressions for the SPPF give very precise results with maximum relativeerrors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions,respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy,chemical potential, heat capacity and pressure are given analytically valid for any scale.
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| 2. |
- Aydin, Alhun, et al.
(author)
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Discrete and Weyl density of states for photonic dispersion relation
- 2019
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In: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 94:10
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Journal article (peer-reviewed)abstract
- The current density of states (DOS) calculations do not take into account the essential discretenessof the state space, since they rely on the unbounded continuum approximation. Recently, discrete DOS based on the quantum-mechanically allowable minimum energy interval has been introducedfor quadratic dispersion relation. In this work, we consider systems exhibiting photonic (photon-like) dispersion relation and calculate the related density and number of states (NOS). Also, a Weyl's conjecture-based DOS function is calculated for photons and acoustic phonons at low frequency limit,by considering the bounded continuum approach. We show that discrete DOS function reducesto expressions of bounded and unbounded continua in the appropriate limits. The uctuationsin discrete DOS completely disappear under accumulation operators. It's interesting that relativeerrors of NOS and DOS functions with respect to discrete ones have exactly the same character withthe ones of quadratic dispersion relation. Furthermore, the application of discrete and Weyl DOS for the calculation of internal energy of a photon gas is presented and importance of discrete DOSis discussed. It's shown that discrete DOS function given in this work needs to be used wheneverthe low energy levels of a physical system are heavily occupied.
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| 3. |
- Aydin, Alhun, et al.
(author)
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Discrete Density of States
- 2016
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In: Physics Letters A. - 0375-9601 .- 1873-2429. ; 380, s. 1236-1240
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Journal article (peer-reviewed)abstract
- By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they’re almost completely flattenedout after summation or integration operation. It’s seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl’s conjecture always preserve their lower error characteristic.
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| 4. |
- Aydin, Alhun, et al.
(author)
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Discrete Nature of Thermodynamics in Confined Ideal Fermi Gases
- 2014
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In: Physics Letters A. - 0375-9601 .- 1873-2429. ; 378, s. 2001-2007
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Journal article (peer-reviewed)abstract
- Intrinsic discrete nature in thermodynamic properties of Fermi gas appears in strongly confined and degenerate conditions. For a rectangularconfinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nanodomains; variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that theirrelation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregularoscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors.
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| 5. |
- Aydin, Alhun, et al.
(author)
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Landauer’s Principle in a Quantum Szilard Engine without Maxwell’s Demon
- 2020
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In: Entropy. - : MDPI AG. - 1099-4300. ; 22:3
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Journal article (peer-reviewed)abstract
- Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell’s Demon where Landauer’s principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell’s demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer’s principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer’s principle even in quantum Szilard engines without Maxwell’s demon.
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| 6. |
- Aydin, Alhun, et al.
(author)
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Origin of the quantum shape effect
- 2023
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In: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 108:2
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Journal article (peer-reviewed)abstract
- The quantum size and shape effects are often considered difficult to distinguish from each other because oftheir coexistence. Essentially, it is possible to separate them and focus solely on the shape effect by consideringa size-invariant shape transformation, which changes the discrete energy spectra of strongly confined systemsand causes the quantum shape effects. The size-invariant shape transformation is a geometric technique oftransforming shapes by preserving the boundary curvature, topology, and the Lebesgue measure of a boundeddomain. The quantum shape effect is a quite different phenomenon from quantum size effects, as it can havethe opposite influence on the physical properties of nanoscale systems. While quantum size effects can usuallybe obtained via bounded continuum approximation, the quantum shape effect is a direct consequence of theenergy quantization in specifically designed confined geometries. Here, we explore the origin of the quantumshape effect by theoretically investigating the simplest system that can produce the same physics: quantumparticles in a one-dimensional box separated by a moving partition. The partition moves quasistatically fromone end of the box to the other, allowing the system to remain in equilibrium with a reservoir throughout theprocess. The partition and the boundaries are impenetrable by particles, forming two effectively interconnectedregions. The position of the partition becomes the shape variable.We investigate the quantum shape effect on thethermodynamic properties of confined particles considering their discrete spectrum. In addition, we applied ananalytical model based on dimensional transitions to predict thermodynamic properties under the quantum shapeeffect accurately. A fundamental understanding of quantum shape effects could pave the way for employing themto engineer physical properties and design better materials at the nanoscale.
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| 7. |
- aydin, Alhun, et al.
(author)
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Quantum oscillations in confined and degenerate Fermi gases. I. Half-vicinity model
- 2018
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In: Physics Letters A. - 0375-9601 .- 1873-2429. ; 382, s. 1807-1812
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Journal article (peer-reviewed)abstract
- We propose an analytical model for the prediction and accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate Fermi gases. Our model considers only half-vicinity states of Fermi level. We show that the half-vicinity model quite accurately estimates quantum oscillations depending on confinement and degeneracy. Periods of quantum oscillations are even analytically expressed for one-dimensional case. Furthermore, similarities between functional behaviors of total occupancy variance and conventional density of states functions at Fermi level are discussed.
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| 8. |
- Aydin, Alhun, et al.
(author)
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Quantum oscillations in confined and degenerate Fermi gases. II. The phase diagram and applications of half-vicinity model
- 2018
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In: Physics Letters A. - 0375-9601 .- 1873-2429. ; 382, s. 1813-1817
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Journal article (peer-reviewed)abstract
- For part I see DOI: 10 .1016 /j.physleta.2018.02.006. Size and density dependent quantum oscillations appear in Fermi gases under strong confinement and degeneracy conditions. We provide a universal recipe that explicitly separates oscillatory regime from non-oscillatory (stationary) one. A phase diagram representing stationary and oscillatory regimes on degeneracy-confinement space is proposed. Analytical expressions of phase transition interfaces are derived. The critical point, which separates entirely stationary and oscillatory regions, is determined and its dependencies on aspect ratios are examined for anisometric domains. Accuracy of the half-vicinity model and the phase diagram are verified through the quantum oscillations in electronic heat capacity and its ratio to entropy.
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| 9. |
- Aydin, Alhun, et al.
(author)
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Quantum shape effects and novel thermodynamic behaviors at nanoscale
- 2019
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In: Physics Letters A. - : Elsevier BV. - 0375-9601 .- 1873-2429. ; 383:7, s. 655-665
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Journal article (peer-reviewed)abstract
- Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schrödinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features.
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| 10. |
- Aydin, Alhun, et al.
(author)
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Quantum shape oscillations in the thermodynamic properties of confined electrons in core–shell nanostructures
- 2021
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In: Journal of Physics. - : Institute of Physics Publishing (IOPP). - 0953-8984 .- 1361-648X. ; 34:2
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Journal article (peer-reviewed)abstract
- Quantum shape effect appears under the size-invariant shape transformations of stronglyconfined structures. Such a transformation distinctively influences the thermodynamicproperties of confined particles. Due to their characteristic geometry, core–shellnanostructures are good candidates for quantum shape effects to be observed. Here weinvestigate the thermodynamic properties of non-interacting degenerate electrons confined incore–shell nanowires consisting of an insulating core and a GaAs semiconducting shell. Wederive the expressions of shape-dependent thermodynamic quantities and show the existenceof a new type of quantum oscillations due to shape dependence, in chemical potential, internalenergy, entropy and specific heat of confined electrons.We provide physical understanding ofour results by invoking the quantum boundary layer concept and evaluating the distributions ofquantized energy levels on Fermi function and in state space. Besides the density, temperatureand size, the shape per se also becomes a control parameter on the Fermi energy of confinedelectrons, which provides a new mechanism for fine tuning the Fermi level and changing thepolarity of semiconductors.
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