Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (18)

Search Parameters:
Keywords = dephasing environments

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
16 pages, 1330 KB  
Article
Ergotropy from Geometric Phases in a Dephasing Qubit
by Fernando C. Lombardo and Paula I. Villar
Quantum Rep. 2026, 8(1), 13; https://doi.org/10.3390/quantum8010013 - 12 Feb 2026
Viewed by 655
Abstract
We analyze the geometric phase and dynamic phase acquired by a qubit coupled to an environment through pure dephasing, establishing a direct connection between phase accumulation and ergotropy. We show that the dynamic phase depends solely on the incoherent ergotropy, reflecting its purely [...] Read more.
We analyze the geometric phase and dynamic phase acquired by a qubit coupled to an environment through pure dephasing, establishing a direct connection between phase accumulation and ergotropy. We show that the dynamic phase depends solely on the incoherent ergotropy, reflecting its purely energetic origin. In contrast, the geometric phase exhibits a nontrivial dependence on both the coherent and incoherent contributions to the total ergotropy, encoding the interplay between coherence, dissipation, and energy extraction. By performing a perturbative expansion in the qubit–environment coupling strength, we demonstrate that, in the weak-coupling and long-time regime, the geometric phase becomes determined exclusively by the incoherent ergotropy, which coincides with the asymptotic value of the total ergotropy reached under decoherence. These results provide a clear physical distinction between dynamic and geometric phases in open quantum systems and establish geometric phases as sensitive probes of energetic resources. Furthermore, in superconducting circuit implementations, our findings suggest that the ergotropy of a two-level system could be inferred indirectly from geometric-phase measurements using standard techniques such as quantum state tomography. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
Show Figures

Figure 1

20 pages, 7353 KB  
Article
Comparative Analysis of Robust Entanglement Generation in Engineered XX Spin Chains
by Eduardo K. Soares, Gentil D. de Moraes Neto and Fabiano M. Andrade
Entropy 2025, 27(7), 764; https://doi.org/10.3390/e27070764 - 18 Jul 2025
Viewed by 756
Abstract
We present a numerical investigation comparing two entanglement generation protocols in finite XX spin chains with varying spin magnitudes (s=1/2,1,3/2). Protocol 1 (P1) relies on staggered couplings to steer correlations toward [...] Read more.
We present a numerical investigation comparing two entanglement generation protocols in finite XX spin chains with varying spin magnitudes (s=1/2,1,3/2). Protocol 1 (P1) relies on staggered couplings to steer correlations toward the ends of the chain. At the same time, Protocol 2 (P2) adopts a dual-port architecture that uses optimized boundary fields to mediate virtual excitations between terminal spins. Our results show that P2 consistently outperforms P1 in all spin values, generating higher-fidelity entanglement in shorter timescales when evaluated under the same system parameters. Furthermore, P2 exhibits superior robustness under realistic imperfections, including diagonal and off-diagonal disorder, as well as dephasing noise. To further assess the resilience of both protocols in experimentally relevant settings, we employ the pseudomode formalism to characterize the impact of non-Markovian noise on the entanglement dynamics. Our analysis reveals that the dual-port mechanism (P2) remains effective even when memory effects are present, as it reduces the excitation of bulk modes that would otherwise enhance environment-induced backflow. Together, the scalability, efficiency, and noise resilience of the dual-port approach position it as a promising framework for entanglement distribution in solid-state quantum information platforms. Full article
(This article belongs to the Special Issue Entanglement in Quantum Spin Systems)
Show Figures

Figure 1

14 pages, 465 KB  
Article
Quantum W-Type Entanglement in Photonic Systems with Environmental Decoherence
by Kamal Berrada and Smail Bougouffa
Symmetry 2025, 17(7), 1147; https://doi.org/10.3390/sym17071147 - 18 Jul 2025
Viewed by 1042
Abstract
Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. [...] Read more.
Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. Using the lower bound of concurrence (LBC) as a measure of entanglement, we analyze the time evolution of the LBC for photons initially prepared in a W state under the influence of dephasing noise. We explore the dependence of entanglement dynamics on system parameters such as the dephasing angle and refractive-index difference, alongside environmental spectral properties. Our results, obtained within experimentally feasible parameter ranges, reveal how the enhancement of entanglement preservation can be achieved in Markovian and non-Markovian regimes according to the system parameters. These findings provide valuable insights into the robustness of W-state entanglement in tripartite photonic systems and offer practical guidance for optimizing quantum protocols in noisy environments. Full article
Show Figures

Figure 1

21 pages, 1969 KB  
Article
Manipulating Entanglement Dynamics in Dephased Interacting Qubits Using a Radiation Field
by Omar Qisieh, Rahma Abdelmagid and Gehad Sadiek
Entropy 2025, 27(7), 673; https://doi.org/10.3390/e27070673 - 24 Jun 2025
Viewed by 1088
Abstract
We study the entanglement dynamics of a pair of non-identical interacting atoms (qubits) coupled off-resonance to a single-mode cavity radiation field and exposed to dephasing environments. The qubits are studied starting from various initial states that are disentangled from an initially coherent field. [...] Read more.
We study the entanglement dynamics of a pair of non-identical interacting atoms (qubits) coupled off-resonance to a single-mode cavity radiation field and exposed to dephasing environments. The qubits are studied starting from various initial states that are disentangled from an initially coherent field. The system models the basic building units of quantum information processing (QIP) platforms under the realistic considerations of asymmetry and external environmental influences. We investigate how introducing a radiation field alters the system’s entanglement dynamics in the presence of dephasing environments, and how it impacts the effects of the dephasing environments themselves. The work examines the problem under various settings of inter-qubit interactions, which are now experimentally controllable in some of the newly engineered artificial qubit systems. We illustrate that only upon introducing the radiation field, the system suffers a terminal disentanglement (followed by no revivals) in a finite time. This behavior is exacerbated when the atoms’ interaction with the field is stronger. Moreover, the effects of the field’s intensity and the atoms’ detunings are vastly sensitive to the choice of the initial state. We also demonstrate that the closer the atoms’ transition frequencies are to resonance with the field, the more pronounced are the effects of strengthening the independent dephasing environments corresponding to some initial states. Those states also suffered a greater reduction in entanglement content when the qubits with stronger atom–field interaction strength were influenced by a stronger independent dephasing environment. In addition, we examined the ability of the correlated dephasing environment to induce a noise-enhanced efficiency in the presence of an external radiation field. We showed that the radiation field could play a decisive role in enabling or restricting noise-enhanced efficiency, but one that is also highly sensitive to the system’s initial state. Full article
(This article belongs to the Section Quantum Information)
Show Figures

Figure 1

12 pages, 483 KB  
Article
Quantum Steering and Fidelity in a Two-Photon System Subjected to Symmetric and Asymmetric Phasing Interactions
by Kamal Berrada and Smail Bougouffa
Symmetry 2025, 17(5), 647; https://doi.org/10.3390/sym17050647 - 25 Apr 2025
Cited by 1 | Viewed by 840
Abstract
This paper examines the dynamics of quantum steering and fidelity in a two-photon system subjected to dephasing interactions, examining their behavior in Markovian and non-Markovian environments. We consider the case of identical and distinct dephasing rates with experimental parameter values to ensure that [...] Read more.
This paper examines the dynamics of quantum steering and fidelity in a two-photon system subjected to dephasing interactions, examining their behavior in Markovian and non-Markovian environments. We consider the case of identical and distinct dephasing rates with experimental parameter values to ensure that the analysis reflects realistic conditions, enhancing its relevance to practical quantum systems. Quantum steering, the ability to remotely influence a quantum state, and fidelity, a measure of initial-state preservation, are investigated for time evolution, initial-state configuration, dephasing parameters, and system characteristics. We model each photon as independently interacting with its environment and derive the time-evolved reduced-density matrix for the bipartite system, focusing on how environmental effects shape the system’s behavior. By integrating experimentally feasible parameter values, this work establishes a practical framework for tuning quantum steering and fidelity, providing valuable insights for applications in quantum information processing, such as secure communication and state preservation. Full article
Show Figures

Figure 1

14 pages, 12042 KB  
Article
Tightly Trapped Atom Interferometer inside a Hollow-Core Fiber
by Yitong Song, Wei Li, Xiaobin Xu, Rui Han, Chengchun Gao, Cheng Dai and Ningfang Song
Photonics 2024, 11(5), 428; https://doi.org/10.3390/photonics11050428 - 3 May 2024
Cited by 6 | Viewed by 2982
Abstract
We demonstrate a fiber-guided atom interferometer in a far-off-resonant trap (FORT) of 100 μK. The differential light shift (DLS) introduced by the FORT leads to the inhomogeneous dephasing of the tightly trapped atoms inside a hollow-core fiber. The DLS-induced dephasing is greatly suppressed [...] Read more.
We demonstrate a fiber-guided atom interferometer in a far-off-resonant trap (FORT) of 100 μK. The differential light shift (DLS) introduced by the FORT leads to the inhomogeneous dephasing of the tightly trapped atoms inside a hollow-core fiber. The DLS-induced dephasing is greatly suppressed in π/2-π-π/2 Doppler-insensitive interferometry. The spin coherence time is extended to 13.4 ms by optimizing the coupling of the trapping laser beam into a quasi-single-mode hollow-core anti-resonant fiber. The Doppler-sensitive interferometry shows a much shorter coherence time, indicating that the main limits to our fiber-guided atom interferometer are the wide axial velocity distribution and the irregular modes of the Raman laser beams inside the fiber. This work paves the way for portable and miniaturized quantum devices, which have advantages for inertial sensing at arbitrary orientations and in dynamic environments. Full article
(This article belongs to the Special Issue The Integration of Quantum Communication and Quantum Sensors)
Show Figures

Figure 1

16 pages, 1497 KB  
Article
Geometric Phase of a Transmon in a Dissipative Quantum Circuit
by Ludmila Viotti, Fernando C. Lombardo and Paula I. Villar
Entropy 2024, 26(1), 89; https://doi.org/10.3390/e26010089 - 22 Jan 2024
Cited by 1 | Viewed by 3517
Abstract
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, [...] Read more.
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment. Full article
Show Figures

Figure 1

15 pages, 1607 KB  
Article
Entanglement Degradation in Two Interacting Qubits Coupled to Dephasing Environments
by Rahma Abdelmagid, Khadija Alshehhi and Gehad Sadiek
Entropy 2023, 25(10), 1458; https://doi.org/10.3390/e25101458 - 17 Oct 2023
Cited by 4 | Viewed by 2812
Abstract
One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence [...] Read more.
One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state. Full article
Show Figures

Figure 1

14 pages, 541 KB  
Article
Dephasing Dynamics in a Non-Equilibrium Fluctuating Environment
by Xiangjia Meng, Yaxin Sun, Qinglong Wang, Jing Ren, Xiangji Cai and Artur Czerwinski
Entropy 2023, 25(4), 634; https://doi.org/10.3390/e25040634 - 8 Apr 2023
Cited by 5 | Viewed by 2288
Abstract
We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, [...] Read more.
We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel. Full article
Show Figures

Figure 1

13 pages, 317 KB  
Article
Robust Semi-Quantum Summation over a Collective-Dephasing Noise Channel
by Chun-Wei Yang, Chia-Wei Tsai, Chi-An Chen and Jason Lin
Mathematics 2023, 11(6), 1405; https://doi.org/10.3390/math11061405 - 14 Mar 2023
Cited by 11 | Viewed by 2205
Abstract
Quantum summation is one of the various applications in secure multi-party computation. However, most of the existing quantum summation protocols assume that the participants possess all the quantum devices. Considering future applications, the capability of the participants must be adjusted before it can [...] Read more.
Quantum summation is one of the various applications in secure multi-party computation. However, most of the existing quantum summation protocols assume that the participants possess all the quantum devices. Considering future applications, the capability of the participants must be adjusted before it can be put into practical use. Although Boyer et al. proposed that the semi-quantum environment could be used to solve this problem; another practical problem is the interference by noise. In 2022, Ye et al. proposed a two-party semi-quantum summation (SQS) protocol resistant to the interference of collective noise, in which two classical participants can accomplish the summation of their private binary sequences with the assistance of a quantum semi-honest third party. They proved that their SQS protocol is resistant to various eavesdropping attacks. This paper unveils two risks of information leakage in Ye et al.’s SQS protocol. If the aforementioned security issues are not resolved, Ye et al.’s SQS protocol may not be able to perform private quantum computations securely. Fortunately, the SQS protocol against the collective-dephasing noise proposed in this study is free from the issue of information leakage as well as resistant to various quantum attacks. In addition, the quantum efficiency of the SQS protocol proposed in this study is four times higher than that of Ye et al.’s SQS protocol, which can effectively improve the quantum utilization rate. Full article
(This article belongs to the Special Issue Quantum Cryptography and Applications)
15 pages, 1421 KB  
Perspective
Optimization of Coherent Dynamics of Localized Surface Plasmons in Gold and Silver Nanospheres; Large Size Effects
by Krystyna Kolwas
Materials 2023, 16(5), 1801; https://doi.org/10.3390/ma16051801 - 22 Feb 2023
Cited by 5 | Viewed by 2114
Abstract
Noble metal nanoparticles have attracted attention in recent years due to a number of their exciting applications in plasmonic applications, e.g., in sensing, high-gain antennas, structural colour printing, solar energy management, nanoscale lasing, and biomedicines. The report embraces the electromagnetic description of inherent [...] Read more.
Noble metal nanoparticles have attracted attention in recent years due to a number of their exciting applications in plasmonic applications, e.g., in sensing, high-gain antennas, structural colour printing, solar energy management, nanoscale lasing, and biomedicines. The report embraces the electromagnetic description of inherent properties of spherical nanoparticles, which enable resonant excitation of Localized Surface Plasmons (defined as collective excitations of free electrons), and the complementary model in which plasmonic nanoparticles are treated as quantum quasi-particles with discrete electronic energy levels. A quantum picture including plasmon damping processes due to the irreversible coupling to the environment enables us to distinguish between the dephasing of coherent electron motion and the decay of populations of electronic states. Using the link between classical EM and the quantum picture, the explicit dependence of the population and coherence damping rates as a function of NP size is given. Contrary to the usual expectations, such dependence for Au and Ag NPs is not a monotonically growing function, which provides a new perspective for tailoring plasmonic properties in larger-sized nanoparticles, which are still hardly available experimentally. The practical tools for comparing the plasmonic performance of gold and silver nanoparticles of the same radii in an extensive range of sizes are also given. Full article
(This article belongs to the Special Issue Advances in Nanoscale and Low-Dimensional Functional Materials)
Show Figures

Figure 1

19 pages, 5863 KB  
Article
Composite Discordant States and Quantum Darwinism
by Eoghan Ryan and Mauro Paternostro
Entropy 2022, 24(11), 1509; https://doi.org/10.3390/e24111509 - 22 Oct 2022
Cited by 1 | Viewed by 2099
Abstract
The framework of Quantum Darwinism strives at characterizing the quantum-to-classical transition by introducing the concept of redundancy of information—as measured by Mutual Information—that a set of observers would acquire on the state of a physical system of interest. Further development on this concept, [...] Read more.
The framework of Quantum Darwinism strives at characterizing the quantum-to-classical transition by introducing the concept of redundancy of information—as measured by Mutual Information—that a set of observers would acquire on the state of a physical system of interest. Further development on this concept, in the form of Strong Quantum Darwinism and Spectrum Broadcast Structures, has recently led to a more fine-grained identification of the nature of such information, which should not involve any quantum correlations between observing and observed systems, while the assessment of information proliferation from individual systems has attracted most of the attention so far, the way such mechanism takes place in more complex states is open to exploration. To this end, we shall consider a two-qubit state, sharing initial quantum correlations in the form of Quantum Discord, and different dephasing-like interactions between them and an observing environment. We will focus on the amount of information regarding the subsystem not involved in the interaction that is proliferated to the environment. We shall refer to this as mediated redundancy. We will show that, in some cases, the channel capacity of the subsystems, given these interactions, can exceed that of the fragments. Full article
(This article belongs to the Section Quantum Information)
Show Figures

Figure 1

23 pages, 2648 KB  
Article
Equilibration and “Thermalization” in the Adapted Caldeira–Leggett Model
by Andreas Albrecht
Entropy 2022, 24(3), 316; https://doi.org/10.3390/e24030316 - 23 Feb 2022
Cited by 2 | Viewed by 2809
Abstract
I explore the processes of equilibration exhibited by the Adapted Caldeira–Leggett (ACL) model, a small unitary “toy model” developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety [...] Read more.
I explore the processes of equilibration exhibited by the Adapted Caldeira–Leggett (ACL) model, a small unitary “toy model” developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety of situations. While the finite model size and other “unphysical” aspects prevent the notions of temperature and thermalization from being generally applicable, certain primitive aspects of thermalization can be realized for particular parameter values. I link the observed behaviors to intrinsic properties of the global energy eigenstates, and argue that the phenomena I observe contain elements which might be key ingredients that lead to ergodic behavior in larger more realistic systems. The motivations for this work range from curiosity about phenomena observed in earlier calculations with the ACL model to much larger questions related to the nature of equilibrium, thermalization, and the emergence of physical laws. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Show Figures

Figure 1

15 pages, 9833 KB  
Article
Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models
by Nina Megier, Andrea Smirne, Steve Campbell and Bassano Vacchini
Entropy 2022, 24(2), 304; https://doi.org/10.3390/e24020304 - 21 Feb 2022
Cited by 9 | Viewed by 3357
Abstract
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of [...] Read more.
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
Show Figures

Figure 1

13 pages, 959 KB  
Article
Quantum Darwinism in a Composite System: Objectivity versus Classicality
by Barış Çakmak, Özgür E. Müstecaplıoğlu, Mauro Paternostro, Bassano Vacchini and Steve Campbell
Entropy 2021, 23(8), 995; https://doi.org/10.3390/e23080995 - 31 Jul 2021
Cited by 20 | Viewed by 4776
Abstract
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an [...] Read more.
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Show Figures

Figure 1

Back to TopTop